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: URL:
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.
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.

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.