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This section contains free e-books and guides on Riemannian Geometry, some of the resources in this section can be viewed online and some of them can be downloaded.

Riemannian Geometry Books
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Lectures on Geodesics Riemannian Geometry

PDF | 317 Pages | English
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.

 
Basic Riemannian Geometry

PDF | 29 Pages | English
This note covers the following topics: What is a manifold, Analysis on Riemannian manifolds, Geodesics and curvature, The Bishop volume comparison theorem.

 
Topics in Riemannian Geometry

PDF | 108 Pages | English
The first part of this course note will be a review of some basic concepts in Riemannian geometry. It then gives a fairly basic introduction to the Ricci Flow, some conformal geometry, and look at Riemannian 4-manifolds in greater depth.

 
Riemannian Geometry Lecture Notes

PDF | 107 Pages | English
This lecture note covers the following topics: Riemannian manifolds, Covariant differentiaion, Parallel transport and geodesics, Surfaces in E3 and Curvtature tensor.

 
Riemannian manifolds with geometric structures

PDF | 187 Pages | English
The main aim of this book is to get a way of union of various differential geometric structures on Riemannian manifolds in one scheme.

 
Riemannian Geometry

Online | NA Pages | English
A masterful sourcebook with intriguing exercises, on the theory and application of the tensor calculus, which is indispensable to Riemannian geometry, the Theory of Relativity, and rfiuch of contemporary topology.

 
Lectures on Riemannian Geometry Complex Manifolds

PDF | 38 Pages | English
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.

 
Semi Riemann Geometry and General Relativity

PDF | 251 Pages | English
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, Einsteinís 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.

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

PDF | 59 Pages | English
This note covers the following topics: Smooth manifolds, Riemannian manifolds, Curvature, Space-times, Multilinear Algebra and Non-euclidean geometry.

 
A Course in Riemannian Geometry(Wilkins D.R pdf)

PDF | 72 Pages | English
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.

 
An Introduction to Riemannian Geometry

PDF | 111 Pages | English
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.

 
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