- Title Pages
- Preface
-
1 Smooth manifolds -
2 Matrices and Lie groups -
3 Introduction to vector bundles -
4 Algebra of vector bundles -
5 Maps and vector bundles -
6 Vector bundles with ℂn as fiber -
7 Metrics on vector bundles -
8 Geodesics -
9 Properties of geodesics -
10 Principal bundles -
11 Covariant derivatives and connections -
12 Covariant derivatives, connections and curvature -
13 Flat connections and holonomy -
14 Curvature polynomials and characteristic classes -
15 Covariant derivatives and metrics -
16 The Riemann curvature tensor -
17 Complex manifolds -
18 Holomorphic submanifolds, holomorphic sections and curvature -
19 The Hodge star - List of lemmas, propositions, corollaries and theorems
- List of symbols
- Index
Properties of geodesics
Properties of geodesics
- Chapter:
- (p.96) 9 Properties of geodesics
- Source:
- Differential Geometry
- Author(s):
Clifford Henry Taubes
- Publisher:
- Oxford University Press
This chapter examines the properties of geodesics. It discusses the maximal extension of a geodesic; the exponential map; Gaussian coordinates; and the proof of the geodesic theorem.
Keywords: exponential map, Gaussian coordinates, geodesic theorem
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- Title Pages
- Preface
-
1 Smooth manifolds -
2 Matrices and Lie groups -
3 Introduction to vector bundles -
4 Algebra of vector bundles -
5 Maps and vector bundles -
6 Vector bundles with ℂn as fiber -
7 Metrics on vector bundles -
8 Geodesics -
9 Properties of geodesics -
10 Principal bundles -
11 Covariant derivatives and connections -
12 Covariant derivatives, connections and curvature -
13 Flat connections and holonomy -
14 Curvature polynomials and characteristic classes -
15 Covariant derivatives and metrics -
16 The Riemann curvature tensor -
17 Complex manifolds -
18 Holomorphic submanifolds, holomorphic sections and curvature -
19 The Hodge star - List of lemmas, propositions, corollaries and theorems
- List of symbols
- Index
