Riemannian geometry and geometric analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Ausgabe: | 5. ed. |
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Verlagsinformation Inhaltstext Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 545 - 560 |
| Beschreibung: | XIII, 581 S. graph. Darst. |
| ISBN: | 9783540773405 |
Internformat
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| 245 | 1 | 0 | |a Riemannian geometry and geometric analysis |c Jürgen Jost |
| 250 | |a 5. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XIII, 581 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Universitext | |
| 500 | |a Literaturverz. S. 545 - 560 | ||
| 650 | 4 | |a Geometry, Riemannian | |
| 650 | 0 | 7 | |a Riemannsche Geometrie |0 (DE-588)4128462-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geometrische Analysis |0 (DE-588)4156708-0 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Geometrische Analysis |0 (DE-588)4156708-0 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Geometrische Analysis |0 (DE-588)4156708-0 |D s |
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Datensatz im Suchindex
| _version_ | 1805090076276817920 |
|---|---|
| adam_text |
Contents
1 Foundational Material 1
1.1
Manifolds and Differentiable Manifolds
. 1
1.2
Tangent
Spaces. 6
1.3 Submanifolds. 10
1.4 Riemannian
Metrics
. 13
1.5
Existence of Geodesies on Compact Manifolds
. 28
1.6
The Heat Flow and the Existence of Geodesies
. 31
1.7
Existence of Geodesies on Complete Manifolds
. 34
1.8
Vector Bundles
. 37
1.9
Integral Curves of Vector Fields. Lie Algebras
. 47
1.10
Lie Groups
. 56
1.11
Spin Structures
. 62
Exercises for Chapter
1 . 83
2 De Rham
Cohomology and Harmonic Differential Forms
87
2.1
The Laplace Operator
. 87
2.2
Representing Cohomology Classes by Harmonic Forms
. 96
2.3
Generalizations
. 104
2.4
The Heat Flow and Harmonic Forms
. 105
Exercises for Chapter
2 . 110
3
Parallel Transport, Connections, and Covariant Derivatives
113
3.1
Connections in Vector Bundles
. 113
3.2
Metric Connections. The Yang-Mills Functional
. 124
3.3
The Levi-Civita Connection
. 140
3.4
Connections for Spin Structures and the Dirac Operator
. 155
3.5
The Bochner Method
. 162
3.6
The Geometry of Submanifolds. Minimal Submanifolds
. 164
Exercises for Chapter
3 . 176
4
Geodesies and Jacobi Fields
179
4.1 1st
and
2nd
Variation of Arc Length and Energy
. 179
4.2
Jacobi Fields
. 185
4.3
Conjugate
Points
and Distance Minimizing Geodesies
. 193
4.4
RAemannian Manifolds of Constant Curvature
. 201
4.5
The
Rauch
Comparison Theorems and Other Jacobi Field Estimates
. 203
4.6
Geometric Applications of Jacobi Field Estimates
. 208
4.7
Approximate Fundamental Solutions and Representation Formulae
. . 213
4.8
The Geometry of Manifolds of
Nonpositive
Sectional Curvature
. 215
Exercises for Chapter
4 . 232
A Short Survey on Curvature and Topology
235
5
Symmetric Spaces and
Kahler
Manifolds
243
5.1
Complex
Projective
Space
. 243
5.2 Kahler
Manifolds
. 249
5.3
The Geometry of Symmetric Spaces
. 259
5.4
Some Results about the Structure of Symmetric Spaces
. 270
5.5
The Space Sl(n,»)/SO(n,
Щ
. 277
5.6
Symmetric Spaces of Noncompact Type
. 294
Exercises for Chapter
5 . 299
6
Morse Theory and Ploer Homology
301
6.1
Preliminaries: Aims of Morse Theory
. 301
6.2
The Palais-Smale Condition, Existence of Saddle Points
. 306
6.3
Local Analysis
. 308
6.4
Limits of Trajectories of the Gradient Flow
. 324
6.5
Floer
Condition, Transversality and Z2-Cohomology
. 332
6.6
Orientations and Z-homology
. 338
6.7
Homotopies
. 342
6.8
Graph flows
. 346
6.9
Orientations
. 350
6.10
The Morse Inequalities
. 366
6.11
The Palais-Smale Condition and the Existence of Closed Geodesies
. . 377
Exercises for Chapter
6 . 390
7
Harmonic Maps between Riemannian Manifolds
393
7.1
Definitions
. 393
7.2
Formulae for Harmonic Maps. The Bochner Technique
. 400
7.3
The Energy Integral and Weakly Harmonic Maps
. 412
7.4
Higher Regularity
. 422
7.5
Existence of Harmonic Maps for
Nonpositive
Curvature
. 433
7.6
Regularity of Harmonic Maps for
Nonpositive
Curvature
. 440
7.7
Harmonic Map Uniqueness and Applications
. 459
Exercises for Chapter
7. 466
8
Harmonic maps from Riemann surfaces
469
8.1
Twodimensional Harmonic Mappings
.469
8.2
The Existence of Harmonic Maps in Two Dimensions
.483
8.3
Regularity Results
.504
Exercises for Chapter
8 .517
9
Variational Problems from Quantum Field Theory
521
9.1
The Ginzburg-Landau Functional
.521
9.2
The Seiberg-Witten Functional
.529
9.3
Dirac-harmonic Maps
.536
Exercises for Chapter
9 .543
A Linear Elliptic Partial Differential Equations
545
A.I Sobolev Spaces
.545
A.
2
Linear Elliptic Equations
.549
A.3 Linear Parabolic Equations
.553
В
Fundamental Groups and Covering Spaces
557
Bibliography
560
Index
576 |
| adam_txt |
Contents
1 Foundational Material 1
1.1
Manifolds and Differentiable Manifolds
. 1
1.2
Tangent
Spaces. 6
1.3 Submanifolds. 10
1.4 Riemannian
Metrics
. 13
1.5
Existence of Geodesies on Compact Manifolds
. 28
1.6
The Heat Flow and the Existence of Geodesies
. 31
1.7
Existence of Geodesies on Complete Manifolds
. 34
1.8
Vector Bundles
. 37
1.9
Integral Curves of Vector Fields. Lie Algebras
. 47
1.10
Lie Groups
. 56
1.11
Spin Structures
. 62
Exercises for Chapter
1 . 83
2 De Rham
Cohomology and Harmonic Differential Forms
87
2.1
The Laplace Operator
. 87
2.2
Representing Cohomology Classes by Harmonic Forms
. 96
2.3
Generalizations
. 104
2.4
The Heat Flow and Harmonic Forms
. 105
Exercises for Chapter
2 . 110
3
Parallel Transport, Connections, and Covariant Derivatives
113
3.1
Connections in Vector Bundles
. 113
3.2
Metric Connections. The Yang-Mills Functional
. 124
3.3
The Levi-Civita Connection
. 140
3.4
Connections for Spin Structures and the Dirac Operator
. 155
3.5
The Bochner Method
. 162
3.6
The Geometry of Submanifolds. Minimal Submanifolds
. 164
Exercises for Chapter
3 . 176
4
Geodesies and Jacobi Fields
179
4.1 1st
and
2nd
Variation of Arc Length and Energy
. 179
4.2
Jacobi Fields
. 185
4.3
Conjugate
Points
and Distance Minimizing Geodesies
. 193
4.4
RAemannian Manifolds of Constant Curvature
. 201
4.5
The
Rauch
Comparison Theorems and Other Jacobi Field Estimates
. 203
4.6
Geometric Applications of Jacobi Field Estimates
. 208
4.7
Approximate Fundamental Solutions and Representation Formulae
. . 213
4.8
The Geometry of Manifolds of
Nonpositive
Sectional Curvature
. 215
Exercises for Chapter
4 . 232
A Short Survey on Curvature and Topology
235
5
Symmetric Spaces and
Kahler
Manifolds
243
5.1
Complex
Projective
Space
. 243
5.2 Kahler
Manifolds
. 249
5.3
The Geometry of Symmetric Spaces
. 259
5.4
Some Results about the Structure of Symmetric Spaces
. 270
5.5
The Space Sl(n,»)/SO(n,
Щ
. 277
5.6
Symmetric Spaces of Noncompact Type
. 294
Exercises for Chapter
5 . 299
6
Morse Theory and Ploer Homology
301
6.1
Preliminaries: Aims of Morse Theory
. 301
6.2
The Palais-Smale Condition, Existence of Saddle Points
. 306
6.3
Local Analysis
. 308
6.4
Limits of Trajectories of the Gradient Flow
. 324
6.5
Floer
Condition, Transversality and Z2-Cohomology
. 332
6.6
Orientations and Z-homology
. 338
6.7
Homotopies
. 342
6.8
Graph flows
. 346
6.9
Orientations
. 350
6.10
The Morse Inequalities
. 366
6.11
The Palais-Smale Condition and the Existence of Closed Geodesies
. . 377
Exercises for Chapter
6 . 390
7
Harmonic Maps between Riemannian Manifolds
393
7.1
Definitions
. 393
7.2
Formulae for Harmonic Maps. The Bochner Technique
. 400
7.3
The Energy Integral and Weakly Harmonic Maps
. 412
7.4
Higher Regularity
. 422
7.5
Existence of Harmonic Maps for
Nonpositive
Curvature
. 433
7.6
Regularity of Harmonic Maps for
Nonpositive
Curvature
. 440
7.7
Harmonic Map Uniqueness and Applications
. 459
Exercises for Chapter
7. 466
8
Harmonic maps from Riemann surfaces
469
8.1
Twodimensional Harmonic Mappings
.469
8.2
The Existence of Harmonic Maps in Two Dimensions
.483
8.3
Regularity Results
.504
Exercises for Chapter
8 .517
9
Variational Problems from Quantum Field Theory
521
9.1
The Ginzburg-Landau Functional
.521
9.2
The Seiberg-Witten Functional
.529
9.3
Dirac-harmonic Maps
.536
Exercises for Chapter
9 .543
A Linear Elliptic Partial Differential Equations
545
A.I Sobolev Spaces
.545
A.
2
Linear Elliptic Equations
.549
A.3 Linear Parabolic Equations
.553
В
Fundamental Groups and Covering Spaces
557
Bibliography
560
Index
576 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/73 |
| dewey-search | 516.3/73 |
| dewey-sort | 3516.3 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV023193078 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:05:27Z |
| indexdate | 2024-07-20T09:34:04Z |
| institution | BVB |
| isbn | 9783540773405 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016379433 |
| oclc_num | 231746420 |
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| physical | XIII, 581 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | Springer |
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| series2 | Universitext |
| spelling | Jost, Jürgen 1956- Verfasser (DE-588)115774564 aut Riemannian geometry and geometric analysis Jürgen Jost 5. ed. Berlin [u.a.] Springer 2008 XIII, 581 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Literaturverz. S. 545 - 560 Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Geometrische Analysis (DE-588)4156708-0 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s Geometrische Analysis (DE-588)4156708-0 s 1\p DE-604 DE-604 http://deposit.dnb.de/cgi-bin/dokserv?id=2669086&prov=M&dok_var=1&dok_ext=htm Verlagsinformation text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3030831&prov=M&dok_var=1&dok_ext=htm Inhaltstext http://d-nb.info/986536113/04 Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016379433&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 | Jost, Jürgen 1956- Riemannian geometry and geometric analysis Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd Geometrische Analysis (DE-588)4156708-0 gnd |
| subject_GND | (DE-588)4128462-8 (DE-588)4156708-0 |
| title | Riemannian geometry and geometric analysis |
| title_auth | Riemannian geometry and geometric analysis |
| title_exact_search | Riemannian geometry and geometric analysis |
| title_exact_search_txtP | Riemannian geometry and geometric analysis |
| title_full | Riemannian geometry and geometric analysis Jürgen Jost |
| title_fullStr | Riemannian geometry and geometric analysis Jürgen Jost |
| title_full_unstemmed | Riemannian geometry and geometric analysis Jürgen Jost |
| title_short | Riemannian geometry and geometric analysis |
| title_sort | riemannian geometry and geometric analysis |
| topic | Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd Geometrische Analysis (DE-588)4156708-0 gnd |
| topic_facet | Geometry, Riemannian Riemannsche Geometrie Geometrische Analysis |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2669086&prov=M&dok_var=1&dok_ext=htm http://deposit.dnb.de/cgi-bin/dokserv?id=3030831&prov=M&dok_var=1&dok_ext=htm http://d-nb.info/986536113/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016379433&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT jostjurgen riemanniangeometryandgeometricanalysis |