Homogeneous Geodesics In Homogeneous Riemannian Manifolds Examples

Author : Valerii Berestovskii,Yurii Nikonorov
Publisher : Springer Nature
Page : 482 pages
File Size : 49,9 Mb
Release : 2020-11-05
Category : Mathematics
ISBN : 9783030566586

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Riemannian Manifolds and Homogeneous Geodesics by Valerii Berestovskii,Yurii Nikonorov Pdf

This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses. To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces. The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.

Author : Oldřich Kowalski,Stana Nikčević,Zdeněk Vlášek
Publisher : Unknown
Page : 9 pages
File Size : 41,8 Mb
Release : 2000
Category : Electronic
ISBN : OCLC:76163833

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Homogeneous Geodesics in Homogeneous Riemannian Manifolds - Examples by Oldřich Kowalski,Stana Nikčević,Zdeněk Vlášek Pdf

Author : Peter B. Gilkey
Publisher : World Scientific
Page : 389 pages
File Size : 46,6 Mb
Release : 2007
Category : Science
ISBN : 9781860947858

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The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds by Peter B. Gilkey Pdf

"Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and Stanilov-Tsankov-Videv theory."--BOOK JACKET.

Author : F. Tricerri,L. Vanhecke
Publisher : Cambridge University Press
Page : 145 pages
File Size : 54,6 Mb
Release : 1983-06-23
Category : Mathematics
ISBN : 9780521274890

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Homogeneous Structures on Riemannian Manifolds by F. Tricerri,L. Vanhecke Pdf

The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.

Author : Andreas Arvanitoyeorgos,George Kaimakamis
Publisher : MDPI
Page : 128 pages
File Size : 40,5 Mb
Release : 2020-01-03
Category : Mathematics
ISBN : 9783039280001

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Geometry of Submanifolds and Homogeneous Spaces by Andreas Arvanitoyeorgos,George Kaimakamis Pdf

The present Special Issue of Symmetry is devoted to two important areas of global Riemannian geometry, namely submanifold theory and the geometry of Lie groups and homogeneous spaces. Submanifold theory originated from the classical geometry of curves and surfaces. Homogeneous spaces are manifolds that admit a transitive Lie group action, historically related to F. Klein's Erlangen Program and S. Lie's idea to use continuous symmetries in studying differential equations. In this Special Issue, we provide a collection of papers that not only reflect some of the latest advancements in both areas, but also highlight relations between them and the use of common techniques. Applications to other areas of mathematics are also considered.

Author : Weihuan Chen
Publisher : World Scientific
Page : 368 pages
File Size : 45,7 Mb
Release : 2000
Category : Mathematics
ISBN : 9810244762

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Geometry and Topology of Submanifolds, X by Weihuan Chen Pdf

http://www.worldscientific.com/worldscibooks/10.1142/4569

Author : Andreas Arvanitogeōrgos
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 53,8 Mb
Release : 2003
Category : Homogeneous spaces
ISBN : 9780821827789

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An Introduction to Lie Groups and the Geometry of Homogeneous Spaces by Andreas Arvanitogeōrgos Pdf

It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.

Author : Franco Tricerri,G Tricerri,L. Vanhecke
Publisher : Unknown
Page : 144 pages
File Size : 53,6 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107087309

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Homogeneous Structures on Riemannian Manifolds by Franco Tricerri,G Tricerri,L. Vanhecke Pdf

The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.

Author : W H Chen,C P Wang,A-M Li,U Simon,M Wiehe,L Verstraelen
Publisher : World Scientific
Page : 360 pages
File Size : 47,7 Mb
Release : 2000-11-07
Category : Mathematics
ISBN : 9789814492034

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Geometry and Topology of Submanifolds X by W H Chen,C P Wang,A-M Li,U Simon,M Wiehe,L Verstraelen Pdf

Contents:Progress in Affine Differential Geometry — Problem List and Continued Bibliography (T Binder & U Simon)On the Classification of Timelike Bonnet Surfaces (W H Chen & H Z Li)Affine Hyperspheres with Constant Affine Sectional Curvature (F Dillen et al.)Geometric Properties of the Curvature Operator (P Gilkey)On a Question of S S Chern Concerning Minimal Hypersurfaces of Spheres (I Hiric( & L Verstraelen)Parallel Pure Spinors on Pseudo-Riemannian Manifolds (I Kath)Twistorial Construction of Spacelike Surfaces in Lorentzian 4-Manifolds (F Leitner)Nirenberg's Problem in 90's (L Ma)A New Proof of the Homogeneity of Isoparametric Hypersurfaces with (g,m) = (6, 1) (R Miyaoka)Harmonic Maps and Negatively Curved Homogeneous Spaces (S Nishikawa)Biharmonic Morphisms Between Riemannian Manifolds (Y L Ou)Intrinsic Properties of Real Hypersurfaces in Complex Space Forms (P J Ryan)On the Nonexistence of Stable Minimal Submanifolds in Positively Pinched Riemannian Manifolds (Y B Shen & H Q Xu)Geodesic Mappings of the Ellipsoid (K Voss)η-Invariants and the Poincaré-Hopf Index Formula (W Zhang)and other papers Readership: Researchers in differential geometry and topology. Keywords:Conference;Proceedings;Berlin (Germany);Beijing (China);Geometry;Topology;Submanifolds X;Differential Geometry;Dedication

Author : András Prékopa,Emil Molnár
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 54,5 Mb
Release : 2006-06-03
Category : Mathematics
ISBN : 9780387295558

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Non-Euclidean Geometries by András Prékopa,Emil Molnár Pdf

"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.

Author : A. L. Besse
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 45,9 Mb
Release : 1978-04-01
Category : Mathematics
ISBN : 3540081585

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Manifolds all of whose Geodesics are Closed by A. L. Besse Pdf

X 1 O S R Cher lecteur, J'entre bien tard dans la sphere etroite des ecrivains au double alphabet, moi qui, il y a plus de quarante ans deja, avais accueilli sur mes terres un general epris de mathematiques. JI m'avait parle de ses projets grandioses en promettant d'ailleurs de m'envoyer ses ouvrages de geometrie. Je suis entiche de geometrie et c'est d'elle dontje voudrais vous parler, oh! certes pas de toute la geometrie, mais de celle que fait l'artisan qui taille, burine, amene, gauchit, peaufine les formes. Mon interet pour le probleme dont je veux vous entretenir ici, je le dois a un ami ebeniste. En effet comme je rendais un jour visite il cet ami, je le trouvai dans son atelier affaire a un tour. Il se retourna bientot, puis, rayonnant, me tendit une sorte de toupie et me dit: «Monsieur Besse, vous qui calculez les formes avec vos grimoires, que pensez-vous de ceci?)) Je le regardai interloque. Il poursuivit: «Regardez! Si vous prenez ce collier de laine et si vous le maintenez fermement avec un doigt place n'importe ou sur la toupie, eh bien! la toupie passera toujours juste en son interieur, sans laisser le moindre espace.)) Je rentrai chez moi, fort etonne, car sa toupie etait loin d'etre une boule. Je me mis alors au travail ...

Author : Jes£s A. Alvarez L¢pez,Eduardo Garc¡a-R¡o
Publisher : World Scientific
Page : 343 pages
File Size : 44,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9789814261166

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Differential Geometry by Jes£s A. Alvarez L¢pez,Eduardo Garc¡a-R¡o Pdf

This volume contains research and expository papers on recent advances in foliations and Riemannian geometry. Some of the topics covered in this volume include: topology, geometry, dynamics and analysis of foliations, curvature, submanifold theory, Lie groups and harmonic maps.Among the contributions, readers may find an extensive survey on characteristic classes of Riemannian foliations offering also new results, an article showing the uniform simplicity of certain diffeomorphism groups, an exposition of convergences of contact structures to foliations from the point of view of Thurston's and Thurston?Bennequin's inequalities, a discussion about Fatou?Julia decompositions for foliations and a description of singular Riemannian foliations on spaces without conjugate points.Papers on submanifold theory focus on the existence of graphs with prescribed mean curvature and mean curvature flow for spacelike graphs, isometric and conformal deformations and detailed surveys on totally geodesic submanifolds in symmetric spaces, cohomogeneity one actions on hyperbolic spaces and rigidity of geodesic spheres in space forms. Geometric realizability of curvature tensors and curvature operators are also treated in this volume with special attention to the affine and the pseudo-Riemannian settings. Also, some contributions on biharmonic maps and submanifolds enrich the scope of this volume in providing an overview of different topics of current interest in differential geometry.

Author : Eric Boeckx,Old?ich Kowalski,Lieven Vanhecke
Publisher : World Scientific
Page : 319 pages
File Size : 50,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9789810227685

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Riemannian Manifolds of Conullity Two by Eric Boeckx,Old?ich Kowalski,Lieven Vanhecke Pdf

This book deals with Riemannian manifolds for which the nullity space of the curvature tensor has codimension two. These manifolds are ?semi-symmetric spaces foliated by Euclidean leaves of codimension two? in the sense of Z I Szab¢. The authors concentrate on the rich geometrical structure and explicit descriptions of these remarkable spaces. Also parallel theories are developed for manifolds of ?relative conullity two?. This makes a bridge to a survey on curvature homogeneous spaces introduced by I M Singer. As an application of the main topic, interesting hypersurfaces with type number two in Euclidean space are discovered, namely those which are locally rigid or ?almost rigid?. The unifying method is solving explicitly particular systems of nonlinear PDE.

Author : Miguel Brozos-Vázquez
Publisher : Morgan & Claypool Publishers
Page : 178 pages
File Size : 50,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9781598298192

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The Geometry of Walker Manifolds by Miguel Brozos-Vázquez Pdf

Basic algebraic notions -- Introduction -- A historical perspective in the algebraic context -- Algebraic preliminaries -- Jordan normal form -- Indefinite geometry -- Algebraic curvature tensors -- Hermitian and para-Hermitian geometry -- The Jacobi and skew symmetric curvature operators -- Sectional, Ricci, scalar, and Weyl curvature -- Curvature decompositions -- Self-duality and anti-self-duality conditions -- Spectral geometry of the curvature operator -- Osserman and conformally Osserman models -- Osserman curvature models in signature (2, 2) -- Ivanov-Petrova curvature models -- Osserman Ivanov-Petrova curvature models -- Commuting curvature models -- Basic geometrical notions -- Introduction -- History -- Basic manifold theory -- The tangent bundle, lie bracket, and lie groups -- The cotangent bundle and symplectic geometry -- Connections, curvature, geodesics, and holonomy -- Pseudo-Riemannian geometry -- The Levi-Civita connection -- Associated natural operators -- Weyl scalar invariants -- Null distributions -- Pseudo-Riemannian holonomy -- Other geometric structures -- Pseudo-Hermitian and para-Hermitian structures -- Hyper-para-Hermitian structures -- Geometric realizations -- Homogeneous spaces, and curvature homogeneity -- Technical results in differential equations -- Walker structures -- Introduction -- Historical development -- Walker coordinates -- Examples of Walker manifolds -- Hypersurfaces with nilpotent shape operators -- Locally conformally flat metrics with nilpotent Ricci operator -- Degenerate pseudo-Riemannian homogeneous structures -- Para-Kaehler geometry -- Two-step nilpotent lie groups with degenerate center -- Conformally symmetric pseudo-Riemannian metrics -- Riemannian extensions -- The affine category -- Twisted Riemannian extensions defined by flat connections -- Modified Riemannian extensions defined by flat connections -- Nilpotent Walker manifolds -- Osserman Riemannian extensions -- Ivanov-Petrova Riemannian extensions -- Three-dimensional Lorentzian Walker manifolds -- Introduction -- History -- Three dimensional Walker geometry -- Adapted coordinates -- The Jordan normal form of the Ricci operator -- Christoffel symbols, curvature, and the Ricci tensor -- Locally symmetric Walker manifolds -- Einstein-like manifolds -- The spectral geometry of the curvature tensor -- Curvature commutativity properties -- Local geometry of Walker manifolds with -- Foliated Walker manifolds -- Contact Walker manifolds -- Strict Walker manifolds -- Three dimensional homogeneous Lorentzian manifolds -- Three dimensional lie groups and lie algebras -- Curvature homogeneous Lorentzian manifolds -- Diagonalizable Ricci operator -- Type II Ricci operator -- Four-dimensional Walker manifolds -- Introduction -- History -- Four-dimensional Walker manifolds -- Almost para-Hermitian geometry -- Isotropic almost para-Hermitian structures -- Characteristic classes -- Self-dual Walker manifolds -- The spectral geometry of the curvature tensor -- Introduction -- History -- Four-dimensional Osserman metrics -- Osserman metrics with diagonalizable Jacobi operator -- Osserman Walker type II metrics -- Osserman and Ivanov-Petrova metrics -- Riemannian extensions of affine surfaces -- Affine surfaces with skew symmetric Ricci tensor -- Affine surfaces with symmetric and degenerate Ricci tensor -- Riemannian extensions with commuting curvature operators -- Other examples with commuting curvature operators -- Hermitian geometry -- Introduction -- History -- Almost Hermitian geometry of Walker manifolds -- The proper almost Hermitian structure of a Walker manifold -- Proper almost hyper-para-Hermitian structures -- Hermitian Walker manifolds of dimension four -- Proper Hermitian Walker structures -- Locally conformally Kaehler structures -- Almost Kaehler Walker four-dimensional manifolds -- Special Walker manifolds -- Introduction -- History -- Curvature commuting conditions -- Curvature homogeneous strict Walker manifolds -- Bibliography.

Author : F. Tricerri,L. Vanhecke
Publisher : Cambridge University Press
Page : 144 pages
File Size : 50,5 Mb
Release : 1983-06-23
Category : Mathematics
ISBN : 0521274893

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Homogeneous Structures on Riemannian Manifolds by F. Tricerri,L. Vanhecke Pdf

The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.