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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 
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
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
This note covers the following topics: What is a manifold, Analysis on Riemannian manifolds, Geodesics and curvature, The Bishop volume comparison theorem.
Author(s): F.E. Burstall
29 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
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
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 PagesAdvertisement
