Math 930: Riemannian Geometry I
Instructor: Xiaodong Wang
- Office: D202 Wells Hall
- Phone:
(517) 353-5414
- Fax: (517) 432-1562
- Email: xwang@math.msu.edu
Lectures: TR 3:00 PM - 4:20 PM in A128 WH
Office Hours: MW 2:00-3:30PM or by appointment
Textbook:S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, 3rd edition, Springer, 2004.
References:
- M. P. do Carmo, Riemannina Geometry, Birkhauser, 1992.
- P. Petersen, Riemannian Geometry, 3rd edition, Springer, 2016
Syllabus:
- Riemannian metric and Levi-Civita connection
- curvature tensor
- distance, the exponential map and completeness (Hopf-Rinow)
- geodesics and Jacobi fields
- first and second variation formulas of length
- Bonnet-Myers Theorem and Synge theorem
- Comparison theorems
Exam: There will be a take home final.
Grading: Homework 60% and take home final 40% .
Handout:
Homework: