MAT 458E - Riemannian Geometry

Course Objectives

Transformation of coordinates, covariant and contravariant tensors, metric tensor , Riemannian
metric, Riemannian space, Christoffel 3-index symbols, covariant differentiation, Levi-Civita
connection, curvature of a curve, geodesics, parallel transport , geodesic and Riemannian
coordinates, Riemann curvature tensor, Ricci tensor, special Riemannian spaces (Einstein,
Symmetric, Recurrent etc.). Hypersurfaces of Riemannian spaces; second fundamental form,
Gauss and Mainardi- Codazzi equations

Course Description

To provide a knowledge of the intrinsic geometry of Riemannian manifolds by using
tensors,
2. To provide a knowledge of the geometry of subspaces by using generalized covariant
differentiation,
3. To teach some special Riemannian spaces