Riemannian Geometry by Eckhard Meinrenken

Riemannian Geometry by Shiping Liu USTC

This PDF covers the following topics related to Riemannian Geometry : Introduction, Riemannian Metric, Geodesics, Connections, Curvatures, Space forms and Jacobi fields, Comparison Theorem, Candidates for Synthetic Curvature Conditions.

Author(s): Shiping Liu, Department of Mathematics, USTC

218 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 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

Lecture Notes Riemannian Geometry By Andreas Strombergsson

This note explains the following topics: Manifolds, Tangent spaces and the tangent bundle, Riemannian manifolds, Geodesics, The fundamental group. The theorem of Seifert-van Kampen, Vector bundles, The Yang-Mills functional, Curvature of Riemannian manifolds, Jacobi Fields, Conjugate points.

Author(s): Andreas Strombergsson

241 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

Lectures on Geodesics Riemannian Geometry

Aim of this book is to give a fairly complete treatment of the foundations of Riemannian geometry through the tangent bundle and the geodesic flow on it. Topics covered includes: Sprays, Linear connections, Riemannian manifolds, Geodesics, Canonical connection, Sectional Curvature and metric structure.

Author(s): M. Berger

317 Pages

Riemannian Geometry (Moller J.M pdf)

This note covers the following topics: Smooth manifolds, Riemannian manifolds, Curvature, Space-times, Multilinear Algebra and Non-euclidean geometry.

Author(s): Jesper Michael Moller

59 Pages

An Introduction to Riemannian Geometry

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

Author(s): Sigmundur Gudmundsson

111 Pages