An obstruction to the existence of Einstein metrics on 4-manifolds
An obstruction to the existence of Einstein metrics on 4-manifolds
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4 流形上爱因斯坦度量存在的障碍
DOI：
10.1007/s002080050199
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发表时间：
1998
影响因子：
1.4
通讯作者：
Andrea Sambusetti
中科院分区：
文献类型：
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作者：
Andrea Sambusetti
我们发现了紧致四维流形上爱因斯坦度量存在的一个拓扑障碍，该度量允许非零度映射到紧致实或复双曲四维流形上。因此，通过连通和和通过炸毁复杂的双曲曲面，我们产生了一个不允许爱因斯坦度规但不能从著名的Thorpe-Hitchin或Gromov的阻塞定理中推导出来的4-流形的本质。我们还证明了任何欧拉特征和任何签名都可以通过不含爱因斯坦度规的流形同时实现。
We nd a topological obstruction to the existence of Einstein metrics on compact 4-manifolds which admit a non-zero degree map onto some compact real or complex hyperbolic 4-manifold. As a consequence, by connected sums and by blowing up complex hyperbolic surfaces, we produce an innity of 4-manifolds which admit no Einstein metric but such that this cannot be deduced from the celebrated Thorpe-Hitchin’s or Gromov’s obstruction theorems. We also prove that any Euler characteristic and any signature may be simultaneously realized by manifolds admitting no Einstein metric.