ENGLISH

Aspects of Differential Geometry

By Rámon Vázquez-Lorenzo , JeongHyeong Park , Peter Gilkey

Book information

Publisher
Morgan & Claypool
Year
2015
ISBN
9781627056632
Language
english
Format
PDF
Filesize
3 MB (3563093 bytes)
Series
SYNTHESIS LECTURES ON MATHEMATICS AND STATISTICS #15
Volume
I
Edition
1
Pages
156\156
Time added
2019-09-02 08:53:58

Description

Front Cover......Page 1 Half-Title......Page 3 Copyright......Page 6 Title......Page 7 ABSTRACT, KEYWORDS......Page 8 Contents......Page 11 Preface......Page 13 Acknowledgments......Page 15 1.1 Metric Spaces......Page 17 1.2 Linear Algebra......Page 19 1.3 The Derivative......Page 23 1.4 The Inverse and Implicit Function Theorems......Page 28 1.5 The Riemann Integral......Page 39 2.1 Smooth Manifolds......Page 69 2.2 The Tangent and Cotangent Bundles......Page 77 2.3 Stokes' Theorem......Page 86 2.4 Applications of Stokes' Theorem......Page 100 3.1 The Pseudo-Riemannian Measure......Page 107 3.2 Connections......Page 111 3.3 The Levi–Civita Connection......Page 116 3.4 Geodesics......Page 119 3.5 The Jacobi Operator......Page 126 3.6 The Gauss–Bonnet Theorem......Page 133 3.7 The Chern–Gauss–Bonnet Theorem......Page 142 Bibliography......Page 147 Authors' Biographies......Page 151 Index......Page 153

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