Examples of Einstein manifolds in odd dimensions

Dezhong Chen

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arXiv · 1103.0817

Examples of Einstein manifolds in odd dimensions

Dezhong Chen

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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.

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Dezhong Chen. 2011-03-04. Examples of Einstein manifolds in odd dimensions. https://arxiv.org/abs/1103.0817

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