Riemannian Geometry
by Ilkka Holopainen, Tuomas Sahlsten
2013
Number of pages: 102
Description:
Based on the lecture notes on differential geometry. From the table of contents: Differentiable manifolds, a brief review; Riemannian metrics; Connections; Geodesics; Curvature; Jacobi fields; Curvature and topology; Comparison geometry; The sphere theorem.
Download or read it online for free here:
Download link
(1.3MB, PDF)
Similar books
![Book cover: Medians and Means in Riemannian Geometry: Existence, Uniqueness and Computation](images/blank.gif)
by M. Arnaudon, F. Barbaresco, L. Yang - arXiv
This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. The existence and uniqueness results of local medians are given. We propose a subgradient algorithm and prove its convergence.
(10089 views)
![Book cover: Riemannian Geometry](images/8776.jpg)
by Richard L. Bishop - arXiv
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It starts with the definition of Riemannian and semi-Riemannian structures on manifolds.
(9913 views)
![Book cover: A Course in Riemannian Geometry](images/5712.jpg)
by David R. Wilkins - Trinity College, Dublin
From the table of contents: Smooth Manifolds; Tangent Spaces; Affine Connections on Smooth Manifolds; Riemannian Manifolds; Geometry of Surfaces in R3; Geodesics in Riemannian Manifolds; Complete Riemannian Manifolds; Jacobi Fields.
(11667 views)
![Book cover: Semi-Riemann Geometry and General Relativity](images/blank.gif)
by Shlomo Sternberg
Course notes for 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.
(18515 views)