Manifolds All Of Whose Geodesics Are Closed

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Manifolds All Of Whose Geodesics Are Closed

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Author : A. L. Besse
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Manifolds All Of Whose Geodesics Are Closed written by A. L. Besse and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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 ...

Manifolds All Of Whose Geodesics Are Closed

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Author : Arthur L. Besse
language : de
Publisher:
Release Date : 1978

Manifolds All Of Whose Geodesics Are Closed written by Arthur L. Besse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.

Riemannian Manifolds And Homogeneous Geodesics

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Author : Valerii Berestovskii
language : en
Publisher: Springer Nature
Release Date : 2020-11-05

Riemannian Manifolds And Homogeneous Geodesics written by Valerii Berestovskii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-05 with Mathematics categories.

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.

Differential Geometry And Mathematical Physics

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Author : M. Cahen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Differential Geometry And Mathematical Physics written by M. Cahen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.

This volume contains the text of the lectures which were given at the Differential Geometry Meeting held at Liege in 1980 and at the Differential Geometry Meeting held at Leuven in 1981. The first of these meetings was more orientated toward mathematical physics; the second has a stronger flavour of analysis. The Editors are pleased to thank the lectures who contributed scientifically to these two meetings. They are also grateful to Professor M. F1ato who has encouraged publication of these contributions in the Mathematical Physics Studies Series. We also thank the F.N.R.S. who supported financially the Contact group in differential geometry. The Universite de Liege and the Katholieke Universiteit Leuven which have given us a warm hospitality have contributed to the success of these meetings. We express our gratitude. The Editors. M. Caken et al. (6ds.), Differential Geametry and Mathematical Physics, vii. vii Copyright e 1983 by D. Reidel Publishing Company. Lectures given at the Meeting of the Belgian Contact Group on Differential Geometry held at Liege, May 2-3,1980 SIMULTANEOUS DEFORMATIONS OF A LIE ALGEBRA AND ITS MODULES D. Arnal University of Dijon INTRODUCTION We expose here some results which are obtained by a team at the University of Dijon. This team included Jean-Claude Cortet, Georges Pinczon and myself.

Eigenfunctions Of The Laplacian On A Riemannian Manifold

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Author : Steve Zelditch
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-12

Eigenfunctions Of The Laplacian On A Riemannian Manifold written by Steve Zelditch and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-12 with Mathematics categories.

Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.

Riemannian Geometry

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Author : Isaac Chavel
language : en
Publisher: Cambridge University Press
Release Date : 1995-01-27

Riemannian Geometry written by Isaac Chavel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-27 with Mathematics categories.

This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and those new notions and ideas motivated by curvature itself. Isoperimetric inequalities--the interplay of curvature with volume of sets and the areas of their boundaries--is reviewed along with other specialized classical topics. A number of completely new themes are created by curvature: they include local versus global geometric properties, that is, the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. Also featured is an ambitious "Notes and Exercises" section for each chapter that will develop and enrich the reader's appetite and appreciation for the subject.

Groups Geometric Analysis

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Author :
language : en
Publisher: Academic Press
Release Date : 1984-06-30

Groups Geometric Analysis written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-06-30 with Mathematics categories.

Groups & Geometric Analysis

Groups And Geometric Analysis

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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-17

Groups And Geometric Analysis written by Sigurdur Helgason and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-17 with Mathematics categories.

Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis. Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces.

A Panoramic View Of Riemannian Geometry

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Author : Marcel Berger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

A Panoramic View Of Riemannian Geometry written by Marcel Berger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. These results are stated without detailed proofs but the main ideas involved are described and motivated. This enables the reader to obtain a sweeping panoramic view of almost the entirety of the field. However, since a Riemannian manifold is, even initially, a subtle object, appealing to highly non-natural concepts, the first three chapters devote themselves to introducing the various concepts and tools of Riemannian geometry in the most natural and motivating way, following in particular Gauss and Riemann.

Riemannian Geometry

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Author : Sylvestre Gallot
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Riemannian Geometry written by Sylvestre Gallot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Traditional point of view: pinched manifolds 147 Almost flat pinching 148 Coarse point of view: compactness theorems of Gromov and Cheeger 149 K. CURVATURE AND REPRESENTATIONS OF THE ORTHOGONAL GROUP Decomposition of the space of curvature tensors 150 Conformally flat manifolds 153 The second Bianchi identity 154 CHAPITRE IV : ANALYSIS ON MANIFOLDS AND THE RICCI CURVATURE A. MANIFOLDS WITH BOUNDARY Definition 155 The Stokes theorem and integration by parts 156 B. BISHOP'S INEQUALITY REVISITED 159 Some commutations formulas Laplacian of the distance function 160 Another proof of Bishop's inequality 161 The Heintze-Karcher inequality 162 C. DIFFERENTIAL FORMS AND COHOMOLOGY The de Rham complex 164 Differential operators and their formal adjoints 165 The Hodge-de Rham theorem 167 A second visit to the Bochner method 168 D. BASIC SPECTRAL GEOMETRY 170 The Laplace operator and the wave equation Statement of the basic results on the spectrum 172 E. SOME EXAMPLES OF SPECTRA 172 Introduction The spectrum of flat tori 174 175 Spectrum of (sn, can) F. THE MINIMAX PRINCIPLE 177 The basic statements VIII G. THE RICCI CURVATURE AND EIGENVALUES ESTIMATES Introduction 181 Bishop's inequality and coarse estimates 181 Some consequences of Bishop's theorem 182 Lower bounds for the first eigenvalue 184 CHAPTER V : RIEMANNIAN SUBMANIFOLDS A. CURVATURE OF SUBMANIFOLDS Introduction 185 Second fundamental form 185 Curvature of hypersurfaces 187 Application to explicit computations of curvature 189 B. CURVATURE AND CONVEXITY 192 The Hadamard theorem C.