W. M. Boothby, Introduction to Differentiable Manifolds and Riemannian Geometry (djvu)

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

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

A Course in Riemannian Geometry(Wilkins D.R pdf)

This note covers the following topics, Smooth Manifolds, Tangent Spaces, Affine Connections on Smooth Manifolds, Riemannian Manifolds, Geometry of Surfaces in R3, Geodesics in Riemannian Manifolds, Complete Riemannian Manifolds and Jacobi Fields.

Author(s): David R. Wilkins

72 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