English

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