Riemannian geometry:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Edition: | 3. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 322 S. graph. Darst. |
| ISBN: | 9783540204930 3540204938 |
Staff View
MARC
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| 100 | 1 | |a Gallot, Sylvestre |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Riemannian geometry |c Sylvestre Gallot ; Dominique Hulin ; Jacques Lafontaine |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
| 300 | |a XV, 322 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 700 | 1 | |a Hulin, Dominique |e Verfasser |4 aut | |
| 700 | 1 | |a Lafontaine, Jacques |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804132754749652992 |
|---|---|
| adam_text | Contents
Differential
l.A
l.A.l Submanifolds of Euclidean spaces
I.A.2
1.A.3 Smooth maps
l.B The tangent bundle
l.B.l Tangent space to a submanifold of Rn+k
l.B.
1.B.3 Vector bundles
1.B.4 Tangent map
l.C Vector fields
l.C.l Definitions
l.C.
1.C.3 Integral curves and flow of a vector field
l.C.
l.D Baby Lie groups
l.D.l Definitions
1.D.2 Adjoint representation
l.E Covering maps and fibrations
I.E.I Covering maps and quotients by a discrete group
I.E.
1.E.3 Homogeneous spaces
l.F Tensors
l.F.l Tensor product (a digest)
1.F.2 Tensor bundles
1.F.3 Operations on tensors
1.F.4 Lie derivatives
l.F.
l.F.
l.G Differential forms
l.G.l Definitions
XII Contents
1.G.2 Exterior derivative
1.G.3 Volume
1.G.4
1.G.5
l.H Partitions of unity
2
2.A Existence theorems and first examples
2.A.1 Basic definitions
2.A.2 Submanifolds of Euclidean or Minkowski spaces
2.A.3 Riemannian submanifolds, Riemannian products
2.A.4 Riemannian covering maps, flat tori
2.A.5 Riemannian submersions, complex
2.A.6 Homogeneous Riemannian spaces
2.B Covariant derivative
2.B.1 Connections
2.B.2 Canonical connection of a Riemannian submanifold
2.B.3 Extension of the covariant derivative to tensors
2.B.4 Covariant derivative along a curve
2.B.5 Parallel transport
2.B.6 A natural metric on the tangent bundle
2.C Geodesies
2.
2.C.2 Local existence and uniqueness for geodesies,
exponential map
2.C.3 Riemannian manifolds as metric spaces
2.C.4 An invitation to isosystolic inequalities
2.C.5 Complete Riemannian manifolds, Hopf-Rinow theorem
2.C.6 Geodesies and submersions, geodesies of PnC:
2.C.7 Cut-locus
2.C.8 The geodesic flow
2.
2.D.1 What remains true?
2.D.2 Space, time and light-like curves
2.D.3 Lorentzian analogs of Euclidean spaces, spheres and
hyperbolic spaces
2.D.4 (Incompleteness
2.D.5 The
2.D.6
3
3.
3.A.1 Second covariant derivative
3.A.2 Algebraic properties of the curvature tensor
3.A.3 Computation of curvature: some examples
3.A.4
Contents XIII
З.В
3.B.1 Technical preliminaries
3.B.2 First variation formula
3.B.3 Second variation formula
3.C Jacobi vector fields
3.C.1 Basic topics about second derivatives
3.C.2 Index form
3.C.3 Jacobi fields and exponential map
3.C.4 Applications
3.D Riemannian submersions and curvature
3.D.1 Riemannian submersions and connections
3.D.2 Jacobi fields of PnC
3.D.3 O Neill s formula
3.D.4 Curvature and length of small circles.
Application to Riemannian submersions
3.E The behavior of length and energy in the neighborhood
of a geodesic
3.E.1 Gauss lemma
3.E.2 Conjugate points
3.E.3 Some properties of the cut-locus
3.F Manifolds with constant sectional curvature
3.G Topology and curvature: two basic results
3.G.1 Myers theorem
3.G.2 Cartan-Hadamard s theorem
3.H Curvature and volume
3.H.1 Densities on a differentiable manifold
3.H.2 Canonical measure of a Riemannian manifold
3.H.3 Examples: spheres, hyperbolic spaces, complex
projective
3.H.4 Small balls and scalar curvature
3.H.5 Volume estimates
3.1
3.1.1
3.1.2
manifolds with negative curvature
3.J Curvature and topology: some important results
3.J.1 Integral formulas
3.J.2 (Geo)metric methods
3.J.3 Analytic methods
3.J.4 Coarse point of view: compactness theorems
3.K Curvature tensors and representations of the orthogonal group
3.K.1 Decomposition of the space of curvature tensors
3.K.2 Conformally flat manifolds
3.K.3 The Second
XIV Contents
3.L
3.L.1 Introduction
3.L.2 Angles and distances in the hyperbolic plane
3.L.3 Polygons with many right angles
3.L.4 Compact surfaces
3.L.5 Hyperbolic trigonometry
3.L.6 Prescribing constant negative curvature
3.L.7 A few words about higher dimension
3.M
3.M.1 Introduction
3.M.2 The
3.M.3
4
4.A Manifolds with boundary
4.A.1 Definition
4.
4.
4.B.1 Some commutation formulas
4.B.2 Laplacian of the distance function
4.B.3 Another proof of Bishop s inequality
4.B.4 Heintze-Karcher inequality
4.C Differential forms and cohomology
4.C.1 The
4.C.2 Differential operators and their formal
4.C.3 The Hodge-de Rham theorem
4.C.4 A second visit to the Bochner method
4.D Basic spectral geometry
4.D.1 The Laplace operator and the wave equation
4.D.2 Statement of basic results on the spectrum
4.E Some examples of spectra
4.E.1 Introduction
4.E.2 The spectrum of flat tori
4.E.3 Spectrum of (Sn, can)
4.
4.
4.
4.G.2 Bishop s inequality and coarse estimates
4.G.3 Some consequences of Bishop s theorem
4.G.4 Lower bounds for the first eigenvalue
4.H Paul Levy s isoperimetric inequality
4.H.1 The statement
4.H.2 The proof
Contents
5 Riemannian submanifolds..................................245
5.
5.
5.A.2 Curvature of hypersurfaces
5.A.3 Application to explicit computations of curvatures
5.B Curvature and convexity
5.
5.C.1 First results
5.C.2 Surfaces with constant mean curvature
A Some extra problems
В
Bibliography
Index
List of figures
|
| any_adam_object | 1 |
| author | Gallot, Sylvestre Hulin, Dominique Lafontaine, Jacques |
| author_facet | Gallot, Sylvestre Hulin, Dominique Lafontaine, Jacques |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 537f |
| ctrlnum | (OCoLC)56333747 (DE-599)BVBBV019333830 |
| dewey-full | 516.3/73 |
| 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 |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV019333830 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:57:51Z |
| institution | BVB |
| isbn | 9783540204930 3540204938 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012798726 |
| oclc_num | 56333747 |
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| physical | XV, 322 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Gallot, Sylvestre Verfasser aut Riemannian geometry Sylvestre Gallot ; Dominique Hulin ; Jacques Lafontaine 3. ed. Berlin [u.a.] Springer 2004 XV, 322 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Geometri, Riemannian Riemann-vlakken gtt Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s DE-604 Hulin, Dominique Verfasser aut Lafontaine, Jacques Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012798726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gallot, Sylvestre Hulin, Dominique Lafontaine, Jacques Riemannian geometry Geometri, Riemannian Riemann-vlakken gtt Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4128462-8 |
| title | Riemannian geometry |
| title_auth | Riemannian geometry |
| title_exact_search | Riemannian geometry |
| title_full | Riemannian geometry Sylvestre Gallot ; Dominique Hulin ; Jacques Lafontaine |
| title_fullStr | Riemannian geometry Sylvestre Gallot ; Dominique Hulin ; Jacques Lafontaine |
| title_full_unstemmed | Riemannian geometry Sylvestre Gallot ; Dominique Hulin ; Jacques Lafontaine |
| title_short | Riemannian geometry |
| title_sort | riemannian geometry |
| topic | Geometri, Riemannian Riemann-vlakken gtt Geometry, Riemannian Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Geometri, Riemannian Riemann-vlakken Geometry, Riemannian Riemannsche Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012798726&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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