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.
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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).
by D. Bao, R. Bryant, S. Chern, Z. Shen - Cambridge University Press
Finsler geometry generalizes Riemannian geometry in the same sense that Banach spaces generalize Hilbert spaces. The contributors consider issues related to volume, geodesics, curvature, complex differential geometry, and parametrized jet bundles.
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.
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.