MATH 521: RIEMANNIAN GEOMETRY
Spring 2008

9-10.20 a.m., Tu Th
343 Altgeld Hall

Instructor:
Stephanie Alexander, Professor
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street (MC-382)
Urbana, Illinois 61801-2975

Office: 322 Illini Hall
Phone: (217) 244-7339
FAX:  (217) 333-9576
e-mail: sba@math.uiuc.edu

Riemannian geometry is the core area for modern geometric studies. It has seen recent spectacular successes -- it was a central ingredient of Perelman's solution of the PoincarŽ conjecture. The subject interacts closely with topology and PDE, and has lively interactions with many other areas, including geometric group theory, physics, control theory. Curvature will be our main theme. We cover connections; geodesics; sectional, Ricci and scalar curvature; the Jacobi equation; variations of energy; global comparison and structure theorems. We work in the settings of Riemannian, Lorentz, Alexandrov and CAT(K) spaces.

Prerequisites: Basic manifold theory, namely, differentiable manifolds and vector fields as in Ch. 0 of the text by do Carmo.

Text: Required: Riemannian Geometry, Manfredo doCarmo, Birkhauser,1992. Reference, on reserve in Library: Semi-Riemannian Geometry with Applications to Relativity, Barrett O'Neill, Academic Press, 1983.

Last updated 011/05/07