Einstein metrics and smooth structures
微分几何
2014-11-11 v1 几何拓扑
摘要
We prove that there are infinitely many pairs of homeomorphic non-diffeomorphic smooth 4-manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4-manifolds with two smooth structures which admit Einstein metrics with opposite signs of the scalar curvature.
引用
@article{arxiv.math/9801156,
title = {Einstein metrics and smooth structures},
author = {D. Kotschick},
journal= {arXiv preprint arXiv:math/9801156},
year = {2014}
}
备注
10 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper1.abs.html