by Ilkka Holopainen, Tuomas Sahlsten
Number of pages: 102
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:
by John Douglas Moore - University of California
Foundations of Riemannian geometry, including geodesics and curvature, as well as connections in vector bundles, and then go on to discuss the relationships between curvature and topology. Topology will presented in two dual contrasting forms.
by M. Berger - Tata Institute of Fundamental Research
The main topic of these notes is geodesics. Our aim is to give a fairly complete treatment of the foundations of Riemannian geometry and to give global results for Riemannian manifolds which are subject to geometric conditions of various types.
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 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.