Course Program

Differential Manifolds
Vector Fields and derivations
Lie products and derivatives
Frobenius' Theorem
Differential forms and Tensor Calculus
Integration on Manifolds
Stokes' Theorem
Co-area formula
Lie Groups
Basic notions on Riemannian metrics
Applications

Bibliographic references

M. Spivak: A Comprehensive Introduction to Differential
Geometry, Vol. 1, 3rd Edition, Publish or Perish, 1999.
F. Warner:Foundations of Differentiable Manifolds and Lie
Groups, Springer GTM, 1983.
R. Abraham, J. Marsden, T. Ratiu: Manifolds, Tensor
Analysis, and Applications, 2nd Edition. Springer, Appl.
Math. Sci., 1988.

ExamOral exam

Prerequisites

Differential and integral calculus in one or more variables
Linear algebra
Basic notions in Topology