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Course Information

Course Name
Turkish Differansiyel Geometri I
English Differential Geometry I
Course Code
MAT 511E Credit Lecture
Semester 1
3 3 - -
Course Language English
Course Coordinator Zerrin Şentürk
Course Objectives 1. To recall the basic definitions and theorems of topology;
2. To introduce the notions of differentaiable manifold, tangent and cotangent spaces, and smooth maps;
3. To introduce differential geometric structures on hypersurfaces of Euclidean space to study their geometric properties;
4. To introduce tensors and differential forms to develop Riemannian manifolds.
Course Description Topological spaces, differentiable manifolds, tangent space, vector fields, Lie bracket, diffeomorphism, the inverse function theorem, submanifolds, hypersurfaces, standart connection of Euclidean spaces, Weingarten and Gauss maps, tensors and differential forms, Lie derivative, Riemannian connection, Riemannian manifolds.
Course Outcomes M.Sc. students who successfully pass this course gain knowledge, skills and competency in the following subjects;
I. Some basic definitions and theorems of topology;
II. Basic definitions and theorems of differentiable manifolds;
III. Tangent vector fields, smooth maps on manifolds and the inverse function theorem;
IV. Hypersuraces of Euclidean spaces, Gauss and Weingarten maps, Gauss and Codazzi equations and their applications;
V. Tensors, differential forms on manifolds and their properties;
VI. Riemannian manifolds, Riemannian connection and Riemannian curvature tensor.
Required Facilities
Textbook 1. Boothby, W.M. (1975). An Introduction to Differential Manifolds and Riemannian Geometry, Academic Press Inc..
2. Hicks, N. J. (1971). Notes on Differential Geometry, Van Nostrand Reinhold Company.
3. do Carmo, M.P. (1990). Riemannian Geometry, Birkehauser,
4. Kobayashi, S. ve Nomizu, K. (1963). Foundation of Differential Geometry I, Interscience Publishers.
5. Chen, B-Y,( 1973). Geometry of Submanifolds, M. Decker.
Other References
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