Course Title: Riemannian Geometry
Course Number: MATH 6170 - 1
Instructor: Andrejs Treibergs
Days: M, W, F, 12:55-1:45 PM in JWB 333
Office Hours: 10:40-11:30 M, W, F, in JWB 224 (tent.)
Prerequisites: Some knowledge of differentiable manifolds (e.g. MATH 6510-6520 or consent of instructor.)
Text: Manfredo do Carmo, Riemannian Geometry, Birkhäuser, 1992.

This course is useful for students of geometry, nonlinear analysis and general relativity.

We study how curvature affects local and global properties of smooth manifolds. The principal tool is to use the curvature behavior of geodesics, which are length minimizing curves. We shall develop the intrinsic, classical and differential form notations in parallel. Later we hope to mention how to generalize to length spaces satisfying synthetic conditions. We shall follow do Carmo's text for the first part of the course. We shall use notes of Shiohama and notes of Petersen for the second part of the course. Topics include (depending on time):

Last updated: 08 / 17 / 01