Manifolds All Of Whose Geodesics Are Closed

Author : A. L. Besse
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642618765

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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: {laquo}Monsieur Besse, vous qui calculez les formes avec vos grimoires, que pensez-vous de ceci?)) Je le regardai interloque. Il poursuivit: {laquo}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 : Valerii Berestovskii,Yurii Nikonorov
Publisher : Springer Nature
Page : 482 pages
File Size : 49,7 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 : Wilhelm Klingenberg
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 51,8 Mb
Release : 1983
Category : Electronic
ISBN : 0821888986

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Closed Geodesics on Riemannian Manifolds by Wilhelm Klingenberg Pdf

Author : W Klingenberg
Publisher : Unknown
Page : 248 pages
File Size : 55,9 Mb
Release : 1978-01-01
Category : Curves on surfaces
ISBN : 3642618820

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Lectures on Closed Geodesics by W Klingenberg Pdf

Author : Bernard Pullman,Paul O.P. Ts'O,Edward L. Schneider
Publisher : Springer Science & Business Media
Page : 732 pages
File Size : 49,7 Mb
Release : 1985-11-30
Category : Gardening
ISBN : 9027721173

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Interrelationship Among Aging, Cancer and Differentiation by Bernard Pullman,Paul O.P. Ts'O,Edward L. Schneider Pdf

Proceedings of the Eighteenth Jerusalem Symposium on Quantum Chemistry and Biochemistry held in Jerusalem, Israel, April 29-May 2, 1985

Author : A.T. Fomenko
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400930698

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Integrability and Nonintegrability in Geometry and Mechanics by A.T. Fomenko Pdf

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. 1hen one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin' . • 1111 Oulik'. n. . Chi" •. • ~ Mm~ Mu,d. ", Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : Wilhelm Klingenberg (Mathématicien)
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 40,8 Mb
Release : 1983
Category : Mathematics
ISBN : 9780821807033

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Closed Geodesics on Riemannian Manifolds by Wilhelm Klingenberg (Mathématicien) Pdf

Contains expository lectures from the CBMS Regional Conference held at the University of Florida, 1982. This book considers a space formed by various closed curves in which the closed geodesics are characterized as the critical points of a functional, an idea going back to Morse.

Author : Mikhail Gromov
Publisher : Springer Science & Business Media
Page : 594 pages
File Size : 49,5 Mb
Release : 2007-06-25
Category : Mathematics
ISBN : 9780817645830

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Metric Structures for Riemannian and Non-Riemannian Spaces by Mikhail Gromov Pdf

This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.

Author : Franki J.E. Dillen,Leopold C.A. Verstraelen
Publisher : Elsevier
Page : 574 pages
File Size : 54,8 Mb
Release : 2005-11-29
Category : Mathematics
ISBN : 0080461204

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Handbook of Differential Geometry by Franki J.E. Dillen,Leopold C.A. Verstraelen Pdf

In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. 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. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research . Extensive bibliography . Dealing with a diverse range of areas . Starting from the basics

Author : Shiing-Shen Chern,Robert Osserman,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 451 pages
File Size : 40,9 Mb
Release : 1975
Category : Mathematics
ISBN : 9780821802472

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Differential Geometry by Shiing-Shen Chern,Robert Osserman,American Mathematical Society Pdf

Contains sections on Riemannian geometry, Submanifolds, Foliations, Algebraic and piecewise linear topology, Miscellaneous

Author : Shing-tung Yau
Publisher : Princeton University Press
Page : 720 pages
File Size : 48,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881918

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Seminar on Differential Geometry. (AM-102), Volume 102 by Shing-tung Yau Pdf

This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential geometry and partial differential equations include a general survey article by the editor on the relationship of the two fields and more specialized articles on topics including harmonic mappings, isoperimetric and Poincaré inequalities, metrics with specified curvature properties, the Monge-Arnpere equation, L2 harmonic forms and cohomology, manifolds of positive curvature, isometric embedding, and Kraumlhler manifolds and metrics. The articles on differential geometry and mathematical physics cover such topics as renormalization, instantons, gauge fields and the Yang-Mills equation, nonlinear evolution equations, incompleteness of space-times, black holes, and quantum gravity. A feature of special interest is the inclusion of a list of more than one hundred unsolved research problems compiled by the editor with comments and bibliographical information.

Author : BECKENBACH
Publisher : Birkhäuser
Page : 454 pages
File Size : 46,7 Mb
Release : 2013-11-22
Category : Science
ISBN : 9783034863247

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General Inequalities 2 by BECKENBACH Pdf

Author : Robert Brooks,Carolyn Gordon,Peter A. Perry
Publisher : American Mathematical Soc.
Page : 299 pages
File Size : 49,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851852

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Geometry of the Spectrum by Robert Brooks,Carolyn Gordon,Peter A. Perry Pdf

Spectral geometry runs through much of contemporary mathematics, drawing on and stimulating developments in such diverse areas as Lie algebras, graph theory, group representation theory, and Riemannian geometry. The aim is to relate the spectrum of the Laplace operator or its graph-theoretic analogue, the adjacency matrix, to underlying geometric and topological data. This volume brings together papers presented at the AMS-IMS-SIAM Joint Summer Research Conference on Spectral Geometry, held in July 1993 at the University of Washington in Seattle. With contributions from some of the top experts in the field, this book presents an excellent overview of current developments in spectral geometry.

Author : Gabriel P. Paternain
Publisher : Springer Science & Business Media
Page : 160 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461216001

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Geodesic Flows by Gabriel P. Paternain Pdf

The aim of this book is to present the fundamental concepts and properties of the geodesic flow of a closed Riemannian manifold. The topics covered are close to my research interests. An important goal here is to describe properties of the geodesic flow which do not require curvature assumptions. A typical example of such a property and a central result in this work is Mane's formula that relates the topological entropy of the geodesic flow with the exponential growth rate of the average numbers of geodesic arcs between two points in the manifold. The material here can be reasonably covered in a one-semester course. I have in mind an audience with prior exposure to the fundamentals of Riemannian geometry and dynamical systems. I am very grateful for the assistance and criticism of several people in preparing the text. In particular, I wish to thank Leonardo Macarini and Nelson Moller who helped me with the writing of the first two chapters and the figures. Gonzalo Tomaria caught several errors and contributed with helpful suggestions. Pablo Spallanzani wrote solutions to several of the exercises. I have used his solutions to write many of the hints and answers. I also wish to thank the referee for a very careful reading of the manuscript and for a large number of comments with corrections and suggestions for improvement.

Author : Gabriel P. Paternain,Mikko Salo,Gunther Uhlmann
Publisher : Cambridge University Press
Page : 370 pages
File Size : 49,6 Mb
Release : 2023-01-05
Category : Mathematics
ISBN : 9781009041423

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Geometric Inverse Problems by Gabriel P. Paternain,Mikko Salo,Gunther Uhlmann Pdf

This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered include geodesic X-ray transforms, boundary rigidity, tensor tomography, attenuated X-ray transforms and the Calderón problem. The presentation is self-contained and begins with the Radon transform and radial sound speeds as motivating examples. The required geometric background is developed in detail in the context of simple manifolds with boundary. An in-depth analysis of various geodesic X-ray transforms is carried out together with related uniqueness, stability, reconstruction and range characterization results. Highlights include a proof of boundary rigidity for simple surfaces as well as scattering rigidity for connections. The concluding chapter discusses current open problems and related topics. The numerous exercises and examples make this book an excellent self-study resource or text for a one-semester course or seminar.