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 M-573, Syllabus, Description and Links


MATH 573

Differentiable Manifolds

3 hours

Definition and examples of manifolds. Submanifolds, tangent and cotangent bundles, Vector fields, Differential forms, Tensors, Integration on manifolds.


573 ريض

المانيفولدات التفاضلية

3 ساعات

تعريف المانيفولد التفاضلي وأمثلة، المانيفولدات الجزئية، حزم المماسات والمماسات المرافقة، حقول المتجهات، الصيغ التفاضلية، حقول الممتدات، التكامل.


 Recommended Books:

 1) Y. Matsushima, Differentiable manifolds, Marcel Dekker, New York, 1972.

2) F.W. Warner, Foundations of differentiable manifolds and Lie groups, Scot Foresman and Company, 1971


M-573,  Course Description




No. of weeks

Smooth maps, regular and critical point, immersion and submersions, implicit function theorem, charts around critical and regular points.




Tangent and cotangent bundles, smooth vector fields, properties of smooth vector fields, Lie-algebra of smooth vector fields one parameter group of transformations, complete vector fields.




Local one parameter group of local transformations, .f-related vector fields, diffeomorphisms,. Partition of unity.




Differential forms, exterior differentiation of forms, effect of smooth maps on forms,.




Orientation, Volume form, Integration of differential froms with compact support.




For more details of the course click here.




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