240A Winter 2018

240A Winter 2018

Differental Geometry Math 240A
MWF 11:00-11:50 PM,

Instructor: Prof. Joel Hass
Office: 2222 MSB (Mathematical Sciences Building)
Office hours: Monday 1:10-2 PM, Wednesday 10-11:50 AM.
(530) 601-4444 Extension 4003
email: hass(at)math.ucdavis.edu
(In addition, I plan to organize an optional exercise review session each week. The time will depend on when the most people can come.)

Course Contents: The Department syllabus can be found at Math 240a - Syllabus.

Textbook: The textbook for the course is Riemannian Geometry by M. do Carmo.

This book can be very dense, so you can expect to take a lot of time to read a page if you want to fully understand it. There are numerous other books on differential geometry that would be useful to look at. Some worth considering are:
F. W. Warner, "Foundations of Differential Manifolds and Lie Groups";
W. Boothby, "An Introduction to Differentiable Manifolds and Riemannian Geometry";
P. Petersen, "Riemannian Geometry";
J. Jost, "Riemannian Geometry and Geometric Analysis";
I. Chavel, "Riemannian Geometry: A Modern Introduction".
Gallot, Hulin and Lafontaine, Riemannian Geometry
Lee, Riemannian Manifolds: An Introduction to Curvature
A Panoramic View of Riemannian Geometry, Marcel Berger, Springer 2003.
Spivak, A Comprehensive Introduction to Differential Geometry

Notes: You can find many lecture notes on this subject online. For example:

GRADES: There will be a take home exam during Finals week. (40% of grade).

There will also be regular homework assignments (30%) and a project involving presenting a topic (30%). This wll be discussed in class.

Homework Homework will be listed here when assigned.

HW 1, due Monday 1/21: Chapter 1, Exercises 1,2,3,6.

HW 2, Due Monday, 2/12/18, Chapter 2: Exercises 3,4.

HW 3, Due Monday 2/26/18, Chapter 3: Exercises 4, 7.

HW 4, Due Friday, 3/9/18 Chap 3: Exercises 8, 9.

HW 5, Due Friday, 3/16/18 Chap 4: Exercise 4.
Compute all Jacobi fields for the geodesic in Euclidean 3-space R3 given by g(t) = (t,0,0).