Verfügbarkeit: Riemannian manifolds | Technische Universität München

Riemannian manifolds: an introduction to curvature

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Bibliographische Detailangaben
Beteilige Person:	Lee, John M. 1950- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York [u.a.] Springer 1997
Schriftenreihe:	Graduate texts in mathematics 176
Schlagwörter:	Geometría de Riemann Riemannsche Geometrie Krümmung Riemannscher Raum
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007847942&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XV, 224 S. graph. Darst.
ISBN:	9780387983226 038798271X 0387983228

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Datensatz im Suchindex

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adam_text	Contents Preface vii 1 What Is Curvature? 1 The Euclidean Plane 2 Surfaces in Space 4 Curvature in Higher Dimensions 8 2 Review of Tensors, Manifolds, and Vector Bundles 11 Tensors on a Vector Space 11 Manifolds 14 Vector Bundles 16 Tensor Bundles and Tensor Fields 19 3 Definitions and Examples of Riemannian Metrics 23 Riemannian Metrics 23 Elementary Constructions Associated with Riemannian Metrics . 27 Generalizations of Riemannian Metrics 30 The Model Spaces of Riemannian Geometry 33 Problems 43 4 Connections 47 The Problem of Differentiating Vector Fields 48 Connections 49 Vector Fields Along Curves 55 xiv Contents Geodesies 58 Problems 63 5 Riemannian Geodesies 65 The Riemannian Connection 65 The Exponential Map 72 Normal Neighborhoods and Normal Coordinates 76 Geodesies of the Model Spaces 81 Problems 87 6 Geodesies and Distance 91 Lengths and Distances on Riemannian Manifolds 91 Geodesies and Minimizing Curves 96 Completeness 108 Problems 112 7 Curvature 115 Local Invariants 115 Flat Manifolds . 119 Symmetries of the Curvature Tensor 121 Ricci and Scalar Curvatures 124 Problems 128 8 Riemannian Submanifolds 131 Riemannian Submanifolds and the Second Fundamental Form . . 132 Hypersurfaces in Euclidean Space 139 Geometric Interpretation of Curvature in Higher Dimensions . . 145 Problems 150 9 The Gauss Bonnet Theorem 155 Some Plane Geometry 156 The Gauss Bonnet Formula 162 The Gauss Bonnet Theorem 166 Problems 171 10 Jacobi Fields 173 The Jacobi Equation 174 Computations of Jacobi Fields 178 Conjugate Points 181 The Second Variation Formula 185 Geodesies Do Not Minimize Past Conjugate Points 187 Problems 191 11 Curvature and Topology 193 Some Comparison Theorems 194 Manifolds of Negative Curvature 196 Contents xv Manifolds of Positive Curvature 199 Manifolds of Constant Curvature 204 Problems 208 References 209 Index 213
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indexdate	2024-12-20T10:16:11Z
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isbn	9780387983226 038798271X 0387983228
language	English
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publishDate	1997
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series	Graduate texts in mathematics
series2	Graduate texts in mathematics
spellingShingle	Lee, John M. 1950- Riemannian manifolds an introduction to curvature Graduate texts in mathematics Geometría de Riemann Riemannsche Geometrie (DE-588)4128462-8 gnd Krümmung (DE-588)4128765-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd
subject_GND	(DE-588)4128462-8 (DE-588)4128765-4 (DE-588)4128295-4
title	Riemannian manifolds an introduction to curvature
title_auth	Riemannian manifolds an introduction to curvature
title_exact_search	Riemannian manifolds an introduction to curvature
title_full	Riemannian manifolds an introduction to curvature John M. Lee
title_fullStr	Riemannian manifolds an introduction to curvature John M. Lee
title_full_unstemmed	Riemannian manifolds an introduction to curvature John M. Lee
title_short	Riemannian manifolds
title_sort	riemannian manifolds an introduction to curvature
title_sub	an introduction to curvature
topic	Geometría de Riemann Riemannsche Geometrie (DE-588)4128462-8 gnd Krümmung (DE-588)4128765-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd
topic_facet	Geometría de Riemann Riemannsche Geometrie Krümmung Riemannscher Raum
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work_keys_str_mv	AT leejohnm riemannianmanifoldsanintroductiontocurvature

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