Tight And Taut Submanifolds

Author : Nicolaas Hendrik Kuiper
Publisher : Cambridge University Press
Page : 372 pages
File Size : 40,7 Mb
Release : 1997-11-13
Category : Mathematics
ISBN : 0521620473

Get Book

Tight and Taut Submanifolds by Nicolaas Hendrik Kuiper Pdf

First published in 1997, this book contains six in-depth articles on various aspects of the field of tight and taut submanifolds and concludes with an extensive bibliography of the entire field. The book is dedicated to the memory of Nicolaas H. Kuiper; the first paper is an unfinished but insightful survey of the field of tight immersions and maps written by Kuiper himself. Other papers by leading researchers in the field treat topics such as the smooth and polyhedral portions of the theory of tight immersions, taut, Dupin and isoparametric submanifolds of Euclidean space, taut submanifolds of arbitrary complete Riemannian manifolds, and real hypersurfaces in complex space forms with special curvature properties. Taken together these articles provide a comprehensive survey of the field and point toward several directions for future research.

Author : Thomas E. Cecil,Patrick J. Ryan
Publisher : Pitman Advanced Publishing Program
Page : 356 pages
File Size : 40,6 Mb
Release : 1985
Category : Mathematics
ISBN : UCAL:B4980000

Get Book

Tight and Taut Immersions of Manifolds by Thomas E. Cecil,Patrick J. Ryan Pdf

Author : Franki Dillen,Ignace Van de Woestyne,Leopold Verstraelen
Publisher : World Scientific
Page : 324 pages
File Size : 52,6 Mb
Release : 1994-09-30
Category : Electronic
ISBN : 9789814550659

Get Book

Geometry and Topology of Submanifolds, VI by Franki Dillen,Ignace Van de Woestyne,Leopold Verstraelen Pdf

The topics covered are pure differential geometry, especially submanifolds and affine differential geometry, and applications of geometry to human vision, robotics, and gastro-entrology. Contents:A Riemannian Invariant for Submanifolds in Space Forms and Its Applications (B Y Chen)Some Variational Problems in Submanifold Theory (F Dillen)Isoparametric Systems on Symmetric Spaces (S Mullen)Focal Sets in Affine Geometry (R Niebergall  P J Ryan)Buckling Eigenvalues and Variational Problems for Surfaces in the Three Sphere (B Palmer)On Completeness of Compact Lorentzian Manifolds (A Romero & M Sánchez)On Para Sasakian Manifolds (R Rosca)A Unified Equiaffine Theory for Surfaces in R4, Part 1: The Definite Surfaces (C P Wang)Cartan's Method of Moving Frames Applied to the Study of Surfaces in Affine 4-Space (J L Weiner)A Survey on the Theory of Harmonic (Pseudo)-Riemannian Spaces (T J Willmore)Human Representation of Closed Contours (K Waeytens et al)Affine Shape Equivalence (J Wagemans et al)and other papers Readership: Mathematicians and engineers. keywords:

Author : Felix Effenberger
Publisher : Logos Verlag Berlin GmbH
Page : 224 pages
File Size : 52,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9783832527587

Get Book

Hamiltonian Submanifolds of Regular Polytopes by Felix Effenberger Pdf

This work is set in the field of combinatorial topology, sometimes also referred to as discrete geometric topology, a field of research in the intersection of topology, geometry, polytope theory and combinatorics. The main objects of interest in the field are simplicial complexes that carry some additional structure, forming combinatorial triangulations of the underlying PL manifolds. In particular, polyhedral manifolds as subcomplexes of the boundary complex of a convex regular polytope are investigated. Such a subcomplex is called k-Hamiltonian if it contains the full k-skeleton of the polytope. The notion of tightness of a PL-embedding of a triangulated manifold is closely related to its property of being a Hamiltonian subcomplex of some convex polytope. Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplex-wise linear embedding of the triangulation into Euclidean space is ``as convex as possible''. It can thus be understood as a generalization of the concept of convexity. In even dimensions, there exist purely combinatorial conditions which imply the tightness of a triangulation. In this work, other sufficient and purely combinatorial conditions which can be applied to the odd-dimensional case as well are presented.

Author : Jurgen Berndt,Sergio Console,Carlos Enrique Olmos
Publisher : CRC Press
Page : 494 pages
File Size : 49,7 Mb
Release : 2016-02-22
Category : Mathematics
ISBN : 9781482245165

Get Book

Submanifolds and Holonomy by Jurgen Berndt,Sergio Console,Carlos Enrique Olmos Pdf

Submanifolds and Holonomy, Second Edition explores recent progress in the submanifold geometry of space forms, including new methods based on the holonomy of the normal connection. This second edition reflects many developments that have occurred since the publication of its popular predecessor.New to the Second EditionNew chapter on normal holonom

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512336

Get Book

Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : Thomas E. Cecil
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 49,6 Mb
Release : 2007-10-29
Category : Mathematics
ISBN : 9780387746562

Get Book

Lie Sphere Geometry by Thomas E. Cecil Pdf

Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry.

Author : F.J.E. Dillen,L.C.A. Verstraelen
Publisher : Elsevier
Page : 1067 pages
File Size : 41,9 Mb
Release : 1999-12-16
Category : Mathematics
ISBN : 9780080532837

Get Book

Handbook of Differential Geometry, Volume 1 by F.J.E. Dillen,L.C.A. Verstraelen Pdf

In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.

Author : Richard S. Palais,Chuu-lian Terng
Publisher : Springer
Page : 276 pages
File Size : 48,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540459965

Get Book

Critical Point Theory and Submanifold Geometry by Richard S. Palais,Chuu-lian Terng Pdf

Author : Thomas E. Cecil,Patrick J. Ryan
Publisher : Springer
Page : 596 pages
File Size : 51,6 Mb
Release : 2015-10-30
Category : Mathematics
ISBN : 9781493932467

Get Book

Geometry of Hypersurfaces by Thomas E. Cecil,Patrick J. Ryan Pdf

This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hypersurfaces follows with results that are proved in the context of Lie sphere geometry as well as those that are obtained using standard methods of submanifold theory. Next comes a thorough treatment of the theory of real hypersurfaces in complex space forms. A central focus is a complete proof of the classification of Hopf hypersurfaces with constant principal curvatures due to Kimura and Berndt. The book concludes with the basic theory of real hypersurfaces in quaternionic space forms, including statements of the major classification results and directions for further research.

Author : Luc Vrancken
Publisher : Lulu.com
Page : 266 pages
File Size : 49,6 Mb
Release : 2008-06-30
Category : Mathematics
ISBN : 9781847990167

Get Book

Symposium on the Differential Geometry of Submanifolds by Luc Vrancken Pdf

This book contains the proceedings of the «Symposium on differential geometry» which took place at the Université de Valenciennes et du Hainaut Cambrésis from July 3, 2007 until July 7, 2007.The main theme of the conference was the differential geometry of submanifolds. Special emphasis was put on the following topics:Lagrangian immersions, Minimal immersions and constant mean curvature immersions, Harmonic maps and harmonic morphisms, Variational problems, Affine differential geometry. This conference follows the tradition of the conferences in the series of « Geometry and Topology of Submanifolds », which started with the Luminy meeting in 1987 and then continued with various meetings at different places in Europe, such as amongst others Avignon, Leeds, Leuven, Brussels, Nordfjordeid, Berlin, Warszawa, Bedlewo and also in China (Beijing, 1998).

Author : K. Kenmotsu
Publisher : Springer
Page : 138 pages
File Size : 47,9 Mb
Release : 2007-01-05
Category : Mathematics
ISBN : 9783540390657

Get Book

Differential Geometry of Submanifolds by K. Kenmotsu Pdf

Author : Sadahiro Maeda,Yoshihiro Ohnita,Qing-Ming Cheng
Publisher : World Scientific
Page : 308 pages
File Size : 41,8 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9789814566292

Get Book

Differential Geometry of Submanifolds and its Related Topics by Sadahiro Maeda,Yoshihiro Ohnita,Qing-Ming Cheng Pdf

This volume is a compilation of papers presented at the conference on differential geometry, in particular, minimal surfaces, real hypersurfaces of a non-flat complex space form, submanifolds of symmetric spaces and curve theory. It also contains new results or brief surveys in these areas. This volume provides fundamental knowledge to readers (such as differential geometers) who are interested in the theory of real hypersurfaces in a non-flat complex space form. Contents:Homogeneous Submanifolds and Homogeneous Curves in Space Forms (S Maeda)Injectivity Property of Regular Curves and a Sphere Theorem (O Kobayashi)A Family of Complete Minimal Surfaces of Finite Total Curvature with Two Ends (S Fujimori and T Shoda)Minimal Surfaces in the Anti-De Sitter Spacetime (T Ichiyama and S Udagawa)Extrinsic Circular Trajectories on Geodesic Spheres in a Complex Projective Space (T Adachi)Geometry of Certain Lagrangian Submanifolds in Hermitian Symmetric Spaces (Y Ohnita)Some Real Hypersurfaces of Complex Projective Space (T Hamada)Contact Metric Hypersurfaces in Complex Space Forms (J T Cho and J Inoguchi)Non-Homogeneous η-Einstein Real Hypersurfaces in a 2-Dimensional Nonflat Complex Space Form (K Okumura)Sectional Curvatures of Ruled Real Hypersurfaces in a Nonflat Complex Space Form (H Tanabe and S Maeda)Totally Geodesic Köhler Immersions into a Complex Space Form, and a Non-Existence Theorem for Hessian Metrics of Positive Constant Hessian Sectional Curvature (T Noda and N Boumuki)Archimedean Theorems and W-Curves (D-S Kim and Y H Kim)On the Construction of Cohomogeneity One Special Lagrangian Submanifolds in the Cotangent Bundle of the Sphere (K Hashimoto)Self-Shrinkers of the Mean Curvature Flow (Q-M Cheng and Y Peng)Spectrum of Poly-Laplacian and Fractional Laplacian (L Zeng)Flat Centroaffine Surfaces with Non-Semisimple Tchebychev Operator (A Fujioka)The Total Absolute Curvature of Open Curves in EN (K Enomoto and J Itoh)Antipodal Sets of Compact Symmetric Spaces and the Intersection of Totally Geodesic Submanifolds (M S Tanaka)A Note on Symmetric Triad and Hermann Action (O Ikawa)Some Topics of Homogeneous Submanifolds in Complex Hyperbolic Spaces (T Hashinaga, A Kubo and H Tamaru)Austere Hypersurfaces in 5-Sphere and Real Hypersurfaces in Complex Projective Plane (J T Cho and M Kimura)On the Minimality of Normal Bundles in the Tangent Bundles Over the Complex Space Forms (T Kajigaya)Over-Determined Systems on Surfaces (N Ando) Readership: Researchers in differential geometry. Keywords:Minimal Surfaces;Morse Index;Real Hypersurfaces;Non-flat Complex Space Forms;Hopf Hypersurfaces;Symmetric Spaces;Homogeneous CurvesKey Features:Interesting papers on the theory of real hypersurfaces and the theory of minimal surfacesFeatures prominent contributors such as Y Ohnita, Q-M Cheng and O Kobayashi

Author : Wolfgang Kühnel
Publisher : American Mathematical Soc.
Page : 403 pages
File Size : 45,9 Mb
Release : 2015-12-22
Category : Curves
ISBN : 9781470423209

Get Book

Differential Geometry by Wolfgang Kühnel Pdf

This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and--as a new feature--a good number of solutions to selected exercises.

Author : Thomas E. Cecil
Publisher : Halsted Press
Page : 352 pages
File Size : 52,7 Mb
Release : 1986-05-01
Category : Electronic
ISBN : 0470204389

Get Book

Tight and Taut Immersions of Manifolds by Thomas E. Cecil Pdf