PMATH 868Connections and Riemannian Geometry

Review of smooth manifolds. Vector bundles. Connections and curvature, holonomy, characteristic classes. Connections on tangent bundle: torsion, geodesics, exponential map. Riemannian geometry: Levi-Civita connection, Riemannian geodesics, Hopf-Rinow Theorem. Additional topics if time permits. Students are expected to have background in smooth manifolds covering the topics of PMATH 665.