Riemannian Geometry

3 credits · Graduate School

Vector fields, brackets; Riemannian metrics; Riemannian connections; geodesic flow; curvature: sectional curvature, Ricci curvature, scalar curvature; Jacobi fields; Hopf-Rinow Theorem; Hadamard Theorem. Complex manifolds, Hermitian metrics, Kahler metrics, complex projective space, first Chern class of a line bundle. Prerequisite: 270. [3]