Part III - Riemannian Geometry
Lectured by A. G. Kovalev, Lent 2017
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Contents
- V Full version
- 1 Basics of Riemannian manifolds
- 2 Riemann curvature
- 3 Geodesics
- 3.1 Definitions and basic properties
- 3.2 Jacobi fields
- 3.3 Further properties of geodesics
- 3.4 Completeness and the Hopf–Rinow theorem
- 3.5 Variations of arc length and energy
- 3.6 Applications
- 4 Hodge theory on Riemannian manifolds
- 4.1 Hodge star and operators
- 4.2 Hodge decomposition theorem
- 4.3 Divergence
- 4.4 Introduction to Bochner's method
- 5 Riemannian holonomy groups
- 6 The Cheeger–Gromoll splitting theorem