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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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 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).
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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.
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.