Lectures on Geodesics in Riemannian Geometry
by M. Berger
Publisher: Tata Institute of Fundamental Research 1965
Number of pages: 317
The main topic of these notes is geodesics. Our aim is 1) to give a fairly complete treatment of the foundations of Riemannian geometry through the tangent bundle and the geodesic flow on it and 2) to give global results for Riemannian manifolds which are subject to geometric conditions of various types; these conditions involve essentially geodesics.
Download or read it online for free here:
by Curtis McMullen - Harvard University
Contents: Maps between Riemann surfaces; Sheaves and analytic continuation; Algebraic functions; Holomorphic and harmonic forms; Cohomology of sheaves; Cohomology on a Riemann surface; Riemann-Roch; Serre duality; Maps to projective space; etc.
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.
by Adam Marsh - arXiv
A pedagogical but concise overview of Riemannian geometry is provided in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions and relevant theorems.
by 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).