Aspects of Differential Geometry

✍ Scribed by Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo

• Publisher: Morgan & Claypool
• Year: 2015
• Tongue: English
• Leaves: 156
• Series: SYNTHESIS LECTURES ON MATHEMATICS AND STATISTICS #15
• Edition: 1
• Category: Library

✦ Table of Contents

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