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

1.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.