Course Information

Course Name	Turkish	Diferansiyel Geometri I
	English	Differential Geometry I
Course Code	MAT 511E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	1	3	3	-	-
Course Language		English
Course Coordinator		Fatma Özdemir Fatma Özdemir
Course Objectives		1.To introduce the notions of differentaiable manifold, tangent and cotangent spaces, and smooth maps; 2.To introduce differential geometric structures on hypersurfaces of Euclidean space to study their geometric properties; 3.To introduce tensors and differential forms to to develop Riemannian manifolds and submanifolds.
Course Description		Topological Spaces, product topology, metric topology, quotient topology, connectedness, compactness. Differentiable manifolds. Tangent space, vector fields. Lie Bracket., Diffeomorphism, inverse function theorem. Submanifolds. Hypersurfaces, standart connection of Euclidean Spaces. Weingarten and Gauss maps. Tensors and differential forms. Lie Derivative. Riemannian connection, Riemannian manifolds and Riemannian submanifolds.
Course Outcomes		At the end of the course students will have the knowledge on the following conscepts and their applications: I.Elementry general topology; II.Differentiable manifolds, tangent vector fields and smooth maps on manifolds; III.Hypersuraces of Euclidean space, Gauss and Weingarten maps, Gauss and Codazzi equations; IV.Tensors, differential forms and their properties; V.Riemannian manifolds, Riemannian connection and Riemannian curvature tensor.
Pre-requisite(s)		None
Required Facilities
Other
Textbook		William M. Boothby, An Introduction to Differential Manifolds and Riemannian Geometry, 1975. Noel J. Hicks, Notes on Differentail Geometry, 1971. Manfredo P. do Carmo, Riemannian Geometry, 1990. S. Kobayashi and K. Nomizu, Foundation of Differential Geometry I, 1963.
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