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

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 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

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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

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