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

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

Riemannian Geometry Lecture Notes

This lecture note covers the following topics: Riemannian manifolds, Covariant differentiaion, Parallel transport and geodesics, Surfaces in E3 and Curvtature tensor.

Author(s): H.M. Khudaverdian

107 Pages

Riemannian manifolds with geometric structures

The main aim of this book is to get a way of union of various differential geometric structures on Riemannian manifolds in one scheme.

Author(s): Alexander A. Ermolitski

187 Pages

Lectures on Riemannian Geometry Complex Manifolds

This is an introductory lecture note on the geometry of complex manifolds. Topics discussed are: almost complex structures and complex structures on a Riemannian manifold, symplectic manifolds, Kahler manifolds and Calabi-Yau manifolds,hyperkahler geometries.

Author(s): Stefan Vandoren

38 Pages

Semi Riemann Geometry and General Relativity

This book represents course notes for a one semester course at the undergraduate level giving an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus, preferably in the language of differential forms.

Author(s): ShlomoSternberg

251 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