Riemannian Geometry (Moller J.M pdf)

Riemannian Geometry

These lecture notes are based on the course in Riemannian geometry at the University of Illinois over a period of many years. This book contains below topics, Riemannian metrics, Minimizers, Connections, The Riemannian Connection, Calculus of variations, Riemannian curvature, Conjugate Points, Completeness, Curvature and topology.

Author(s): Richard L. Bishop

64 Pages

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 HopfRinow 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

This note covers the following topics, Differentiable Manifolds, The Tangent Space, The Tangent Bundle, Riemannian Manifolds, The LeviCivita Connection, Geodesics, The Riemann Curvature Tensor, Curvature and Local Geometry.

Author(s): Sigmundur Gudmundsson

111 Pages