Course Information

Course Name	Turkish	Riemann Geometrisi
	English	Riemannian Geometry
Course Code	MAT 458E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	-	3	3	-	-
Course Language		English
Course Coordinator		Gülçin Çivi Bilir
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
Course Outcomes		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
Pre-requisite(s)
Required Facilities
Other
Textbook		C.E.Weatherburn Riemannian Geometry and Tensor Calculus, 1966
Other References		L.P.Eisenhart, Riemannian Geometry (Other References) P.D.Carmo, Riemannian Geometry Dodson, C. T. J. ve Poston, T., 1979, ‘Tensor Geometry’, Fearon Pitman Pub Inc. California

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