Comparison theorems in Riemannian geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS Chelsea Publ.
2008
|
| Edition: | Nachdr. der Ausg. Amsterdam 1975 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 161 S. graph. Darst. |
| ISBN: | 9780821844175 |
Staff View
MARC
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| 245 | 1 | 0 | |a Comparison theorems in Riemannian geometry |c Jeff Cheeger ; David G. Ebin |
| 250 | |a Nachdr. der Ausg. Amsterdam 1975 | ||
| 264 | 1 | |a Providence, RI |b AMS Chelsea Publ. |c 2008 | |
| 300 | |a X, 161 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Riemannian manifolds | |
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Record in the Search Index
| _version_ | 1804138135385276416 |
|---|---|
| adam_text | Contents
Preface
to the
AMS
Chelsea Printing
vii
Preface
ix
Chapter
1.
Basic Concepts and Results
1
1.
Notation and preliminaries
1
2.
First variation of arc length
3
3.
Exponential map and normal coordinates
6
4.
The Hopf-Rinow Theorem
9
5.
The curvature tensor and Jacobi fields
11
6.
Conjugate points
14
7.
Second variation of arc length
16
8.
Submanifolds and the second fundamental form
18
9.
Basic index lemmas
20
10.
Ricci
curvature and Myers and Bonnet s Theorems
23
11. Rauch
Comparison Theorem
24
12.
The Cartan-Hadamard Theorem
30
13.
The Cartan-Ambrose-Hicks Theorem
31
14.
Spaces of constant curvature
34
Chapter
2.
Toponogov s Theorem
35
Chapter
3.
Homogeneous Spaces
47
Chapter
4.
Morse Theory
69
Chapter
5.
Closed Geodesies and the Cut Locus
81
Chapter
6.
The Sphere Theorem and its Generalizations
93
Chapter
7.
The Differentiable Sphere Theorem
105
Chapter
8.
Complete Manifolds of
Nonnegative
Curvature
119
Chapter
9.
Compact Manifolds of
Nonpositive
Curvature
137
Bibliography
149
Additional Bibliography
155
Index
157
|
| adam_txt |
Contents
Preface
to the
AMS
Chelsea Printing
vii
Preface
ix
Chapter
1.
Basic Concepts and Results
1
1.
Notation and preliminaries
1
2.
First variation of arc length
3
3.
Exponential map and normal coordinates
6
4.
The Hopf-Rinow Theorem
9
5.
The curvature tensor and Jacobi fields
11
6.
Conjugate points
14
7.
Second variation of arc length
16
8.
Submanifolds and the second fundamental form
18
9.
Basic index lemmas
20
10.
Ricci
curvature and Myers' and Bonnet's Theorems
23
11. Rauch
Comparison Theorem
24
12.
The Cartan-Hadamard Theorem
30
13.
The Cartan-Ambrose-Hicks Theorem
31
14.
Spaces of constant curvature
34
Chapter
2.
Toponogov's Theorem
35
Chapter
3.
Homogeneous Spaces
47
Chapter
4.
Morse Theory
69
Chapter
5.
Closed Geodesies and the Cut Locus
81
Chapter
6.
The Sphere Theorem and its Generalizations
93
Chapter
7.
The Differentiable Sphere Theorem
105
Chapter
8.
Complete Manifolds of
Nonnegative
Curvature
119
Chapter
9.
Compact Manifolds of
Nonpositive
Curvature
137
Bibliography
149
Additional Bibliography
155
Index
157 |
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| edition | Nachdr. der Ausg. Amsterdam 1975 |
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| index_date | 2024-07-02T22:29:24Z |
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| publisher | AMS Chelsea Publ. |
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| spelling | Cheeger, Jeff Verfasser aut Comparison theorems in Riemannian geometry Jeff Cheeger ; David G. Ebin Nachdr. der Ausg. Amsterdam 1975 Providence, RI AMS Chelsea Publ. 2008 X, 161 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geometry, Riemannian Riemannian manifolds Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Riemannscher Raum (DE-588)4128295-4 s DE-604 Riemannsche Geometrie (DE-588)4128462-8 s Ebin, David G. Verfasser aut Erscheint auch als Online-Ausgabe 978-1-4704-3121-1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016814856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cheeger, Jeff Ebin, David G. Comparison theorems in Riemannian geometry Geometry, Riemannian Riemannian manifolds Riemannscher Raum (DE-588)4128295-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4128295-4 (DE-588)4128462-8 (DE-588)4113937-9 |
| title | Comparison theorems in Riemannian geometry |
| title_auth | Comparison theorems in Riemannian geometry |
| title_exact_search | Comparison theorems in Riemannian geometry |
| title_exact_search_txtP | Comparison theorems in Riemannian geometry |
| title_full | Comparison theorems in Riemannian geometry Jeff Cheeger ; David G. Ebin |
| title_fullStr | Comparison theorems in Riemannian geometry Jeff Cheeger ; David G. Ebin |
| title_full_unstemmed | Comparison theorems in Riemannian geometry Jeff Cheeger ; David G. Ebin |
| title_short | Comparison theorems in Riemannian geometry |
| title_sort | comparison theorems in riemannian geometry |
| topic | Geometry, Riemannian Riemannian manifolds Riemannscher Raum (DE-588)4128295-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Geometry, Riemannian Riemannian manifolds Riemannscher Raum Riemannsche Geometrie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016814856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT cheegerjeff comparisontheoremsinriemanniangeometry AT ebindavidg comparisontheoremsinriemanniangeometry |