Einstein metrics and smooth structures
Einstein metrics and smooth structures
复制标题
爱因斯坦度量和平滑结构
DOI：
10.2140/gt.1998.2.1
复制
发表时间：
1998
影响因子：
2
通讯作者：
D. Kotschick
中科院分区：
文献类型：
--
作者：
D. Kotschick
我们证明了存在无穷多对同胚非对胚光滑4{流形，使得在每对流形中，一个流形有爱因斯坦度规而另一个没有。我们还证明了具有两个光滑结构的闭4{流形，它们允许具有相反符号的标量曲率的爱因斯坦度量。
We prove that there are innitely many pairs of homeomorphic non-dieomorphic 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.