# شريف صادق دشموخ

 This Site: شريف صادق دشموخ

Guidelines_English_Final

### Quick Launch

 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

 Topic No. of weeks Smooth maps, regular and critical point, immersion and submersions, implicit function theorem, charts around critical and regular points. 3 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. 3 Local one parameter group of local transformations, .f-related vector fields, diffeomorphisms,. Partition of unity. 3 Differential forms, exterior differentiation of forms, effect of smooth maps on forms,. 3 Orientation, Volume form, Integration of differential froms with compact support. 3

http://en.wikipedia.org/wiki/Manifold

http://www.math.harvard.edu/theses/phd/bloom/ThesisXFinal.pdf

http://www.math.washington.edu/~arms/mpp07/t2sg.pdf

http://www2.maths.ox.ac.uk/~hitchin/hitchinnotes/hitchinnotes.html

### MATH573

 Type
 Name
 Modified By
M-573final(1430)شريف صادق دشموخ
M-573midterm(1430)شريف صادق دشموخ
M-573IIsemesterfinal1429شريف صادق دشموخ