Manifolds all of whose geodesics are closed:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1978
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
93 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 262 S. Ill., graph. Darst. |
| ISBN: | 3540081585 0387081585 |
Internformat
MARC
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| 100 | 1 | |a Besse, Arthur L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Manifolds all of whose geodesics are closed |c Arthur L. Besse |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1978 | |
| 300 | |a IX, 262 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 93 | |
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| 650 | 4 | |a Dynamique topologique | |
| 650 | 7 | |a Dynamique topologique |2 ram | |
| 650 | 4 | |a Géométrie différentielle | |
| 650 | 7 | |a Géométrie différentielle |2 ram | |
| 650 | 7 | |a Manifolds |2 gtt | |
| 650 | 7 | |a Topologische dynamica |2 gtt | |
| 650 | 4 | |a Variétés (Mathématiques) | |
| 650 | 7 | |a Variétés (Mathématiques) |2 ram | |
| 650 | 4 | |a Geodesics (Mathematics) | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Topological dynamics | |
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Datensatz im Suchindex
| _version_ | 1804116709000347648 |
|---|---|
| adam_text | Table of Contents
Chapter 0. Introduction 1
A. Motivation and History 1
B. Organization and Contents 4
C. What is New in this Book? 10
D. What are the Main Problems Today? 11
Chapter 1. Basic Facts about the Geodesic Flow 13
A. Summary 13
B. Generalities on Vector Bundles 14
C. The Cotangent Bundle 17
D. The Double Tangent Bundle 18
E. Riemannian Metrics 21
F. Calculus of Variations 22
G. The Geodesic Flow 28
H. Connectors 32
I. Covariant Derivatives 37
J. Jacobi Fields 42
K. Riemannian Geometry of the Tangent Bundle 46
L. Formulas for the First and Second Variations of the Length of Curves . 48
M. Canonical Measures of Riemannian Manifolds 51
Chapter 2. The Manifold of Geodesies 53
A. Summary 53
B. The Manifold of Geodesies 53
C. The Manifold of Geodesies as a Symplectic Manifold 58
D. The Manifold of Geodesies as a Riemannian Manifold 61
Chapter 3. Compact Symmetric Spaces of Rank one From a Geometric Point
of View 71
A. Introduction 71
B. The Projective Spaces as Base Spaces of the Hopf Fibrations 72
C. The Projective Spaces as Symmetric Spaces 75
VIII Table of Contents
D. The Hereditary Properties of Projective Spaces 78
E. The Geodesies of Projective Spaces 81
F. The Topology of Projective Spaces 83
G. The Cayley Projective Plane 86
Chapter 4. Some Examples of C- and P-Manifolds: Zoll and Tannery Surfaces . 94
A. Introduction 94
B. Characterization of P-Metrics of Revolution on S2 95
C. Tannery Surfaces and Zoll Surfaces Isometrically Embedded in (K? can) 105
D. Geodesies on Zoll Surfaces of Revolution 114
E. Higher Dimensional Analogues of Zoll metrics on S2 119
F. On Conformal Deformations of P-Manifolds: A. Weinstein s Result . . 121
G. The Radon Transform on (S2, can) 123
H. V.Guillemin s Proof of Funk s Claim 126
Chapter 5. Blaschke Manifolds and Blaschke s Conjecture 129
A. Summary 129
B. Metric Properties of a Riemannian Manifold 130
C. The Allamigeon-Warner Theorem 132
D. Pointed Blaschke Manifolds and Blaschke Manifolds 135
E. Some Properties of Blaschke Manifolds 141
F. Blaschke s Conjecture 143
G. The Kahler Case 149
H. An Infinitesimal Blaschke Conjecture 151
Chapter 6. Harmonic Manifolds 154
A. Introduction 154
B. Various Definitions, Equivalences 156
C. Infinitesimally Harmonic Manifolds, Curvature Conditions 160
D. Implications of Curvature Conditions 163
E. Harmonic Manifolds of Dimension 4 166
F. Globally Harmonic Manifolds: Allamigeon s Theorem 170
G. Strongly Harmonic Manifolds 172
Chapter 7. On the Topology of SC- and P-Manifolds 179
A. Introduction 179
B. Definitions 180
C. Examples and Counter-Examples 184
D. Bott-Samelson Theorem (C-Manifolds) 186
E. P-Manifolds 192
F. Homogeneous SC-Manifolds 194
Table of Contents IX
G. Questions 198
H. Historical Note 200
Chapter 8. The Spectrum of P-Manifolds 201
A. Summary 201
B. Introduction 201
C. Wave Front Sets and Sobolev Spaces 203
D. Harmonic Analysis on Riemannian Manifolds 206
E. Propagation of Singularities 208
F. Proof of the Theorem 8.9 (J. Duistermaat and V. Guillemin) 209
G. A.Weinstein s result 210
H. On the First Eigenvalue Xx= x{ 211
Appendix A. Foliations by Geodesic Circles. By D. B. A. Epstein 214
I. A. W.Wadsley s Theorem 214
II. Foliations With All Leaves Compact 221
Appendix B. Sturm-Liouville Equations all of whose Solutions are Periodic after
F. Neuman. By Jean Pierre Bourguignon 225
I. Summary 225
II. Periodic Geodesies and the Sturm-Liouville Equation 225
III. Sturm-Liouville Equations all of whose Solutions are Periodic .... 227
IV. Back to Geometry with Some Examples and Remarks 230
Appendix C. Examples of Pointed Blaschke Manifolds. By Lionel Berard
Bergery 231
I. Introduction 231
II. A. Weinstein s Construction 231
III. Some Applications 234
Appendix D. Blaschke s Conjecture for Spheres. By Marcel Berger 236
I. Results 236
II. Some Lemmas 237
III. Proof of Theorem D.4 241
Appendix E. An Inequality Arising in Geometry. By Jerry L. Kazdan .... 243
Bibliography 247
Notation Index 255
Subject Index 259
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:42:49Z |
| institution | BVB |
| isbn | 3540081585 0387081585 |
| language | English |
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| physical | IX, 262 S. Ill., graph. Darst. |
| publishDate | 1978 |
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| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Besse, Arthur L. Verfasser aut Manifolds all of whose geodesics are closed Arthur L. Besse Berlin [u.a.] Springer 1978 IX, 262 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 93 Differentiaalmeetkunde gtt Dynamique topologique Dynamique topologique ram Géométrie différentielle Géométrie différentielle ram Manifolds gtt Topologische dynamica gtt Variétés (Mathématiques) Variétés (Mathématiques) ram Geodesics (Mathematics) Geometry, Differential Manifolds (Mathematics) Topological dynamics Geodäsie (DE-588)4020202-1 gnd rswk-swf Geschlossene geodätische Linie (DE-588)4157022-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Geschlossene geodätische Linie (DE-588)4157022-4 s DE-604 Geodäsie (DE-588)4020202-1 s Ergebnisse der Mathematik und ihrer Grenzgebiete 93 (DE-604)BV005871160 93 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001480249&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Besse, Arthur L. Manifolds all of whose geodesics are closed Ergebnisse der Mathematik und ihrer Grenzgebiete Differentiaalmeetkunde gtt Dynamique topologique Dynamique topologique ram Géométrie différentielle Géométrie différentielle ram Manifolds gtt Topologische dynamica gtt Variétés (Mathématiques) Variétés (Mathématiques) ram Geodesics (Mathematics) Geometry, Differential Manifolds (Mathematics) Topological dynamics Geodäsie (DE-588)4020202-1 gnd Geschlossene geodätische Linie (DE-588)4157022-4 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| subject_GND | (DE-588)4020202-1 (DE-588)4157022-4 (DE-588)4037379-4 |
| title | Manifolds all of whose geodesics are closed |
| title_auth | Manifolds all of whose geodesics are closed |
| title_exact_search | Manifolds all of whose geodesics are closed |
| title_full | Manifolds all of whose geodesics are closed Arthur L. Besse |
| title_fullStr | Manifolds all of whose geodesics are closed Arthur L. Besse |
| title_full_unstemmed | Manifolds all of whose geodesics are closed Arthur L. Besse |
| title_short | Manifolds all of whose geodesics are closed |
| title_sort | manifolds all of whose geodesics are closed |
| topic | Differentiaalmeetkunde gtt Dynamique topologique Dynamique topologique ram Géométrie différentielle Géométrie différentielle ram Manifolds gtt Topologische dynamica gtt Variétés (Mathématiques) Variétés (Mathématiques) ram Geodesics (Mathematics) Geometry, Differential Manifolds (Mathematics) Topological dynamics Geodäsie (DE-588)4020202-1 gnd Geschlossene geodätische Linie (DE-588)4157022-4 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| topic_facet | Differentiaalmeetkunde Dynamique topologique Géométrie différentielle Manifolds Topologische dynamica Variétés (Mathématiques) Geodesics (Mathematics) Geometry, Differential Manifolds (Mathematics) Topological dynamics Geodäsie Geschlossene geodätische Linie Mannigfaltigkeit |
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