MAT 511E - Differential Geometry I

Course Objectives

1. To recall the basic definitions and theorems of topology;
2. To introduce the notions of differentaiable manifold, tangent and cotangent spaces, and smooth maps;
3. To introduce differential geometric structures on hypersurfaces of Euclidean space to study their geometric properties;
4. To introduce tensors and differential forms to develop Riemannian manifolds.

Course Description

Topological spaces, differentiable manifolds, tangent space, vector fields, Lie bracket, diffeomorphism, the inverse function theorem, submanifolds, hypersurfaces, standart connection of Euclidean spaces, Weingarten and Gauss maps, tensors and differential forms, Lie derivative, R