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	8	3	3	-	-
Course Language		English
Course Coordinator		Fatma Özdemir Fatma Özdemir
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.
Course Outcomes		Students completing this course will be able to : I. apply techniques of tensor calculus to Riemannian Geometry, II. have a knowledge and understanding of basics concepts of Riemannian Geometry III. have an awareness of the some special Riemannian spaces. IV. develope the ability to study subspaces of Riemannian spaces.
Pre-requisite(s)
Required Facilities
Other
Textbook		L.P.Eisenhart, Riemannian Geometry P.D.Carmo, Riemannian Geometry Dodson, C. T. J. ve Poston, T., (1979), ‘Tensor Geometry’, Fearon Pitman Pub Inc. California.
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