Einstein Manifolds

Nachdruck of the 1. Auflage Berlin Heidelberg New York 1987
ISBN: 978-3-540-74120-6
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 510 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 1630 g

Reihe: Classics in Mathematics

Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. Recently, it has produced several striking results, which have been of great interest also to physicists. This Ergebnisse volume is the first book which presents an up-to-date overview of the state of the art in this field. "Einstein Manifold"s is a successful attempt to organize the abundant literature, with emphasis on examples. Parts of it can be used separately as introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.

Zielgruppe

Research

Autoren/Hrsg.

Besse, Arthur L.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie

Inhaltsverzeichnis

Basic Material.- Basic Material (Continued): 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.

Über Autor(innen)

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.