CRN: 77241

Instructor: Professor Michael Kapovich, MSB 2224, kapovich@ucdavis.edu

Office hours: WF, 9:40-10:30 AM.

Textbook:
"Riemannian geometry" by M. do Carmo.

Course overview:
This is introductory course in differential geometry. I
expect that you know basics of differentiable manifolds,
as described in Chapter 0 of do Carmo's book (and
covered in MAT-239). In the class we will cover Chapters
1 through 4 of the textbook plus some extra material on
geometry of general bundles. The main objective of the
course is to introduce Riemannian metrics, connections
and curvature for Riemannian manifolds. All these, are
explained well in the textbook (which is one of the best
Riemannian Geometry introductory textbooks). On few
occasions, I will go outside of the textbook, namely,
when we discuss connections and curvature on other
bundles.

Grading: I will
assign weekly homework, which will be due on Mondays, __in
class__. The homework score will be 70% of your
grade. For the last three weeks of the quarter, I will
give every student a paper in differential geometry to
read. After reading the paper, you will write a 2-page
long description (in your own words) of what is in the
paper (there is no need to understand the details of the
proofs, although it is nice if you can!). This will
count for the remaining 30% of your grade.

**Important dates:**

First day of
classes: Monday, January 6, 2020.

Holidays: MLK Day
(Monday, January 20), President's Day (Monday, February
17).

Last day of classes:
Friday, March 13, 2020.

**ADA Statement:**

The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the quarter to discuss any such accommodations for the course.