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MAT 610E - Differential Geometry II

Course Objectives

Tensor fields, exterior derivative, differential forms and Lie derivative. Connections. Riemannian metric, Riemannian manifold, covariant derivative, parallel translation, geodesics and normal coordinates. Curvature tensors, sectional curvature, Ricci curvature and scalar curvature. Space forms. Conformal changes of Riemannian metric. Riemannian submanifolds, induced connection, second fundamental form. Equations of Gauss, Codazzi and Ricci. Cartan structure equations.

Course Description

1.To recall tensor fields, exterior derivative, differential forms and to introduce Lie derivative, connections, Riemannian metric and Riemannian manifold;
2.To examine covariant derivative, parallel translation, geodesics and normal coordinates and their properties;
3.To teach curvature tensors, sectional curvature, Ricci curvature and scalar curvature and to apply them to space forms;
4.To investigate conformal changes of Riemannian metric;
5.To introduce Riemannian submanifolds, induced connection and second fundamental form, and to obtain equations of Gauss, Codazzi and Ricci and Cartan structure equations.

Course Coordinator
Sezgin Altay Demirbağ
Course Language
English
 
 
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