## Math 8365 Riemannian Geometry

Fall 2019

**Location and time: **Vincent Hall 113, MWF
11:15am-12:05pm

**Text: Riemannian Geometry, 3rd Edition***
* by Peter Petersen

**Text: Comparison Theorems in Riemannian Geometry **
by Jeff Cheeger, David Ebin

**Lecturer: **Tian-Jun Li, Vincent
Hall 260,
(612)625-2036

Email: *tjli@math.umn.edu
* URL:
*http://www.math.umn.edu/~tjli*

Office hours: 12:15-1:15, MF.

**Course Content
**

We will cover Petersen's book in the fall and spring semesters.
Intended for a one year course, this book serves as a single source, introducing students
to the important techniques and theorems, while also containing enough background on advanced topics
to appeal to those students wishing to specialize in Riemannian geometry.
This course will combine both the geometric parts of Riemannian geometry and the
analytic aspects of the theory, while also presenting some up-to-date research.

Topics covered in the fall semester:

Chapter 1. Riemannian Metrics

Chapter 2. Derivatives

Chapter 3. Curvature

Chapter 4. Examples

Chapter 5. Geodesics and Distances

Chapter 6. Sectional Curvature Comparison I

Prerequisites: standard manifold theory,
including such topics as tensors and Stokes theorem.

**Homework
**

Various exercises are scattered throughout the text,
helping motivate readers to deepen their understanding of the subject.
There are a small number of homework assignments.

**Grading
**

The final grade will be based on the completion of the homework assignments and a presentation.
There are no exams in this course.

**Feedback and Questions **

You are very welcome to
visit me during my office hours. You can also make appointments to
see me at other time.