On the Scalar Curvature of Einstein Manifolds
dg-ga
2008-02-03 v1 alg-geom
Algebraic Geometry
Differential Geometry
Abstract
We show that there are high-dimensional smooth compact manifolds which admit pairs of Einstein metrics for which the scalar curvatures have opposite signs. These are counter-examples to a conjecture considered by Besse. The proof hinges on showing that the Barlow surface has small deformations with ample canonical line bundle.
Keywords
Cite
@article{arxiv.dg-ga/9705007,
title = {On the Scalar Curvature of Einstein Manifolds},
author = {Fabrizio Catanese and Claude LeBrun},
journal= {arXiv preprint arXiv:dg-ga/9705007},
year = {2008}
}
Comments
LaTeX. 14 pages