Examples of Einstein manifolds in odd dimensions
Differential Geometry
2011-03-07 v1
Abstract
We construct Einstein metrics of non-positive scalar curvature on certain solid torus bundles over a Fano Kahler-Einstein manifold. We show, among other things, that the negative Einstein metrics are conformally compact, and the Ricci-flat metrics have slower-than-Euclidean volume growth and quadratic curvature decay. Also we construct positive Einstein metrics on certain 3-sphere bundles over a Fano Kahler-Einstein manifold. We classify the homeomorphism and diffeomorphism types of the total spaces when the base is the complex projective plane.
Cite
@article{arxiv.1103.0817,
title = {Examples of Einstein manifolds in odd dimensions},
author = {Dezhong Chen},
journal= {arXiv preprint arXiv:1103.0817},
year = {2011}
}
Comments
To appear in "Annals of Global Analysis and Geometry"