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Riemannian Geometry

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Author(s): A. G. Kovalev, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part III Lecture Notes
Publisher: University of Cambridge
Year: 2017

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied

Basics of Riemannian manifolds
Riemann curvature
Geodesics
Definitions and basic properties
Jacobi fields
Further properties of geodesics
Completeness and the Hopf–Rinow theorem
Variations of arc length and energy
Applications
Hodge theory on Riemannian manifolds
Hodge star and operators
Hodge decomposition theorem
Divergence
Introduction to Bochner's method
Riemannian holonomy groups
The Cheeger–Gromoll splitting theorem
Index