- Piotr Hajlasz
- Office: Thaceray Hall 622
- Office hours: MWF 10-11 am + by appointment.
- E-mail: hajlasz@pitt.edu or hajlasz@gmail.com (preferred one)

The main material for the course will be contained in my notes. Differential Geometry

We will cover the following topics:

- Theory of curves in the Euclidean space (curvature, torsion, Frenet equations, global theory of curves).
- Submanifolds of R^n. Riemannian metric.
- Theory of surfaces in R^3 (first and second fundamental form, curvature, the Gauss Theorema Egregium, covariant derivative, the Gauss-Bonnet theorem, minimal surfaces, surfaces of constant curvature, the Liouville theorem on conformal mappings in R^n, n>2).

- Abstract manifolds, the Sard theorem, the Whitney embedding theorem, degree and the Hopf theorem on homotopic mappings into spheres.
- Vector fields, commutators, the Frobenius theorem.
- Tensors and differential forms, Lie derivative.
- Integration of differential forms, the Stokes theorem.

The homework with due dates will be posted online.

HW#1 Due day: November 8