Differential Geometry
Math 1350 Fall 2011

Instructor
• Piotr Hajlasz
• Office: Thaceray Hall 622
• Office hours: MWF 2-3pm + by appointment.
• E-mail: hajlasz@pitt.edu or hajlasz@gmail.com (preferred one)

Textbook

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

You can also look at my notes from the graduate course.

There are many good textbooks in Differential Geoemtry. Here are some of them, but I will not follow any of them, just my notes. If you like to play with MAPLE I recommend the book by Oprea for the hands-on experience with curves and surfaces on the computer.

M. Do Carmo, Differential geometry of curves and surfaces. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1976.

W. Kuhnel, Differential geometry. Curves—surfaces—manifolds. Student Mathematical Library, 16. American Mathematical Society, Providence, RI, 2002.

J. Oprea, Differential geometry and its applications. Second edition. Classroom Resource Materials Series. Mathematical Association of America, Washington, DC, 2007.

D. J. Struik, Lectures on classical differential geometry. Reprint of the second edition. Dover Publications, Inc., New York, 1988.

We will cover the following topics:
• Theory of curves in $R^2$ and $R^3$ (curvature, torsion, Frenet equations, four vertex theorem, isoperimetric inequality, Fenchel's theorem).
• Theory of surfaces in $R^3$ (first and second fundamental form, curvature, the Gauss Theorema Egregium, covariant derivative, the Gauss-Bonnet theorem, Euler characteristic, minimal surfaces, surfaces of constant curvature).

The grades will be based on the homework. I will probably not return the homework, so you might want to make a copy.

Homework

The homework with due dates will be posted online.

HW#1 Due day: September 16.

HW#2 Due day: September 23.

HW#3 Due day: October 11.

HW#4 Due day: November 7.

HW#5 Due day: November 14.