Manifold Geometry 1

Manifold Geometry(1)

Credit: 4

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Outline of the course

Topological manifold, differentiable manifold, tangent vector, tangent space, differentiable maps between manifolds, immersion and submersion, imbedding, submanifolds, inverse function theorem, vector fields, vector bundle as manifold,Topological group, Lie group, transformation groups, quotient manifold, invariant vector fields, Lie algebra of vector fields on a manifold, manifolds with boundary, tensor fields on manifolds, Riemannian manifold.

Reference

Tu, An introduction to manifolds 

Textbooks

   1)  W. M. Boothby; An introduction to differentiable manifolds and Riemannian geometry

2)  P.  Peterson; Riemannian geometry, 1997

 3)  R. Abraham, J, Marsden, T. Ratiu;  Manifolds, tensor analysis and applications.

4)    Warner, Foundations of differential manifolds and Lie groups.