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
Course Objectives		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 Description		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 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		C.E.Weatherburn Riemannian Geometry and Tensor Calculus
Other References		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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