*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