Einstein Manifolds

- Introduction

- Basic Material

- Basic Material: Kähler Manifolds

- Relativity

- Riemannian Functionals

- Ricci Curvature as a Partial Differential Equation

- Einstein Manifolds and Topology

- Homogeneous Riemannian Manifolds

- Compact Homogeneous Kähler Manifolds

- Riemannian Submersions

- Holonomy Groups

- Kähler-Einstein Metrics and the Calabi Conjecture

- The Moduli Space of Einstein Structures

- Self-Duality

- Quaternion-Kähler-Manifolds

- A Report on the Non-Compact Case

- Generalizations of the Einstein Condition

- Appendix. Sobolev Spaces and Elliptic Operators

- Addendum

- Bibliography

- Notation Index

- Subject Index

Arthur L. Besse Besides his personal work in Riemannian Geometry, Marcel Berger is well known for his persistent and untiring propaganda for the problems he considers to be (and which actually are) natural and fundamental.

In 1975, he convinced his students to organise a workshop about one of his favorite problems, namely to understand manifolds, all of whose geodesics are closed. The workshop took place in Besse-en-Chandesse, a very pleasant village in the centre of France, and turned out to be so successful that a consensus emerged to write a book about this topic. Arthur Besse was born.

At that time, such a first name seemed old-fashioned and funny in France. But why not ? Besides, the association with King Arthur could not be overlooked, since this type of meeting was denoted, by the CNRS, as a "Table Ronde" !

The experience was so enjoyable that Arthur did not stop there, and settled down to write another book.

A preliminary workshop took place in another village, even lovelier than the first: Espalion, in the South-West of France. This second book, Einstein Manifolds, was eventually published in 1987.

Years have passed. Arthur's friends (the list of which can be found in the beginning of his books) haved scattered to various places.

For Arthur himself, who never laid any claim to immortality, it may be time for retirement.

One FAQ. What do Bourbaki and Besse have in common? Hardly anything. Simply that both are mathematicians, of course, and share a taste for working in pleasant and quiet places.