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.
This note covers the following
topics: What is a manifold, Analysis on Riemannian manifolds, Geodesics and
curvature, The Bishop volume comparison theorem.
This lecture note covers
the following topics: Riemannian manifolds, Covariant differentiaion, Parallel
transport and geodesics, Surfaces in E3 and Curvtature tensor.
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.