Basic Riemannian Geometry

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 an introductory Course

This note covers curves and surfaces in the plane and in space, Riemannian manifolds, Connections, Geodesics, The second fundamental form.

Author(s): E P Van Den Ban and E Looijenga

42 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 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