Surveys in Differential Geometry, Vol. 6: Essays on Einstein Manifolds

The Surveys in Differential Geometry are supplements to the Journal of Differential Geometry, which are published by International Press. They include significant invited papers combining original research and overviews of the most current research in specific areas of interest to the growing Journal of Differential Geometry community. The survey volumes serve as continuing references, inspirations for new research, and introductions to the variety of topics of interest to differential geometers. These supplements are published annually since 1999.

In this volume of Surveys in Differential Geometry, we offer a comprehensive overview of the essays on Einstein Manifold. We have organized this volume into a triptych. The first panel depicts the Einstein manifolds of special holonomy. The second panel of our triptych concerns techniques applicable to the study of general Einstein manifolds. The last panel of our triptych harkens back to the physical inspirations of our subject.

It is our fondest hope that this book may play an indirect role in settling fundamental questions by refocusing the attention of the mathematical community on the many open problems in this fascinating and important area of Riemannian geometry.