Ma 157b - Riemannian geometry 2; Spring 2004
Instructor: Danny Calegari
MWF 3:30-5 257 Sloan
Grading policy:
One homework problem will be given out each Monday. This homework
is due at the start of class the following Monday.
Description of course:
This course continues on from 157a. We will study basic structures
in Riemannian geometry, and their interactions with topology and analysis.
Topics to be covered (if time allows):
- Hodge theory
- Curvature tensors (e.g. Ricci, scalar, Weyl) and their meaning
- Complex and Kahler geometry
- Holonomy groups and special geometry
References:
- Besse, Einstein manifolds, Springer-Verlag, Ergeb. der Math. und
ihrer Grenz. 3 1987
- Do Carmo, Riemannian Geometry, Birkhauser, 1993
- Gallot, Hulin and Lafontaine, Riemannian Geometry, Springer-Verlag,
Universitext, Second Edition, 1990 or later
- Gross, Huybrechts, Joyce, Calabi-Yau manifolds and
related geometries, Springer-Verlag, Universitext, 2003
- Kodaira, Complex manifolds and deformations of complex structures,
Springer-Verlag, Grund. der Math. Wissen. 283 1986
- Rosenberg, The Laplacian on a Riemannian manifold, LMS student
texts 31 1997