An Introduction to Riemannian Geometry with Applications to Mechanics and Relativity

Riemannian Geometry by Eckhard Meinrenken

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 Hopf-Rinow Theorem, The curvature tensor, Connections on vector bundles.

Author(s): Eckhard Meinrenken, University of Toronto

58 Pages

Riemannian Geometry University of Chicago

This PDF covers the following topics related to Riemannian Geometry : Smooth manifolds, Some examples, Riemannian metrics, Geodesics, Curvature, Lie groups and homogeneous spaces, Characteristic classes, Hodge theory, Minimal surfaces.

Author(s): Danny Calegari, University of Chicago

54 Pages

An Introduction to Riemannian Geometry with Applications to Mechanics and Relativity

This book covers the following topics: Differentiable Manifolds, Differential Forms, Riemannian Manifolds, Curvature, Geometric Mechanics, Relativity.

Author(s): Leonor Godinho and Jose Natario

272 Pages

Basic Riemannian Geometry

This note covers the following topics: What is a manifold, Analysis on Riemannian manifolds, Geodesics and curvature, The Bishop volume comparison theorem.

Author(s): F.E. Burstall

29 Pages