# Math392C: Riemannian Geometry

## Announcements

No class on April 27. Lewis Bowen will be lecturing about Hodge theory on
May 2 and May 4.

I posted the first chapter of Cheeger-Ebin, which has text related to the
lectures on geodesics, etc.

## Basic Information

Professor: Dan Freed

Class Meetings: TTh 11:00-12:30,
RLM 9.166

Discusion/Office Hours: Wednesdays,
3:00-4:00, RLM 9.162

For more details, see the First Day Handout

## Problem Sets

Problem Set #1

Problem Set #2

Problem Set #3

Problem Set #4

Problem Set #5

Problem Set #6

Problem Set #7

Problem Set #8

Problem Set #9

Problem Set #10

Problem Set #11

Problem Set #12

## Notes

Arun Debray
is posting
notes from the lectures.

Note on fiber bundles and vector
bundles

Remarks on Lecture 2 (1/19)

Remarks on Lecture 3 (1/24)

Remarks on Lecture 6 (2/2)

Remarks on Lecture 7 (2/7)

Remarks on Lecture 10 (2/16)

Remarks on Lecture 13 (2/28)

Remarks on Lecture 15 (3/7)

Remarks on Lecture 24 (4/13)

## Readings

Riemann's 1854 lecture introducing
Riemannian geometry (translation by M. Spivak).

Riemann's 1861 essay introducing
Riemann curvature tensor (translation by M. Spivak).

Warner Chapter 1 on manifolds, including
Lie derivatives and the Frobenius theorem.

Spivak chapters on vector fields and the
Frobenius theorem.

Lawson 1974 survey on foliations.

Warner Chapter 3 on Lie groups.

Spivak chapter on connections on principal
bundles.

Kobayashi-Nomizu chapter on connections on
principal bundles, including material on holonomy.

Singer paper on the Chern connection and
the Levi-Civita connection on Kahler manifolds.

Ambrose-Singer paper on their
holonomy theorem.

Simons paper proving Berger's
holonomy classification theorem.

Cheeger-Ebin Chapter 1 on basic
Riemannian geometry.