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
An Introduction to Riemannian Geometry with Applications to Mechanics and Relativityby Leonor Godinho, Jose Natario
Contents: Differentiable Manifolds; Differential Forms; Riemannian Manifolds; Curvature; Geometric Mechanics; Relativity (Galileo Spacetime, Special Relativity, The Cartan Connection, General Relativity, The Schwarzschild Solution).
(8579 views)
Semi-Riemann Geometry and General Relativityby 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.
(17856 views)
Treatise on Differential Geometry and its role in Relativity Theoryby Subenoy Chakraborty - arXiv.org
These notes will be helpful to undergraduate and postgraduate students in theoretical physics and in applied mathematics. Modern terminology in differential geometry has been discussed in the book with the motivation of geometrical way of thinking.
(2458 views)
Lectures notes on compact Riemann surfacesby Bertrand Eynard - arXiv.org
An introduction to the geometry of compact Riemann surfaces. Contents: Riemann surfaces; Functions and forms on Riemann surfaces; Abel map, Jacobian and Theta function; Riemann-Roch; Moduli spaces; Eigenvector bundles and solutions of Lax equations.
(4871 views)