MATH 521: RIEMANNIAN GEOMETRY
Fall 2006

2-2:50 p.m., M W F
241 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. The subject, which is driven by the intuition of spatial perception, has had spectacular successes. It has lively interactions with other areas inside mathematics (e.g., combinatorial group theory, PDE), and outside (e.g., 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; 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 03/28/06