Differential Geometry

Description

Diffeomorphisms; tangent spaces; metric tensors; Poincaré models; isometries; Lie derivative; Killing vector fields; Levi-Civita connection; covariant differentiation; parallel transport; geodesics; helices and circles in Riemannian 3-manifolds; fundamental differential operators; the Laplace equation; Exponential map; Logarithmic map; first and second variation of the arc length functional; geodesic balls and spheres and their volumes; curvature operator; curvature tensor; sectional curvature; Ricci curvature; scalar curvature; the Einstein tensor; applications to Newtonian mechanics, general relativity, and to Finslerian anisotropic geometric phenomena.