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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.
Other References
 
 
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