Midterm due 11/9/09 .

Monday, 1:25-3:15, N. Masmoudi (fall); J. Cheeger (spring).

Prerequisites: multivariable calculus and linear algebra.

Fall Term

Differentiable manifolds, tangent bundle, embedding theorems, vector fields and differential forms. Riemannian metrics and connections, geodesics, exponential map, and Jacobi fields. Generalizations of differential geometric concepts and applications.

Some Books :

Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques Riemannian geometry. Third edition. Universitext. Springer-Verlag, Berlin, 2004. xvi+322 pp. (on reserve in the library)

Spivak, Michael A comprehensive introduction to differential geometry.

Montiel, Sebastián; Ros, Antonio Curves and surfaces. Second edition. Translated from the 1998 Spanish original by Montiel and edited by Donald Babbitt. Graduate Studies in Mathematics, 69. American Mathematical Society, Providence, RI; Real Sociedad Matemática Española, Madrid, 2009. xvi+376 pp.

Michor, Peter W. Topics in differential geometry. Graduate Studies in Mathematics, 93. American Mathematical Society, Providence, RI, 2008. xii+494 pp.