Riemannian Geometry by Eckhard Meinrenken

Overview & Synopsis

This PDF covers the following topics related to Riemannian Geometry, Manifolds, Examples of manifolds, Submanifolds, Tangent spaces, Tangent map, Tangent bundle, Vector fields as derivations, Flows of vector fields, Geometric interpretation of the Lie bracket, Lie groups and Lie algebras, Frobenius theorem, Riemannian metrics, Existence of Riemannian metrics, Length of curves, Connections and parallel transport, Geodesics, The HopfRinow Theorem, The curvature tensor, Connections on vector bundles.