Four-manifolds of pinched sectional curvature
Four-manifolds of pinched sectional curvature
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DOI：
10.2140/pjm.2022.319.17
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发表时间：
2018-09
影响因子：
0.6
通讯作者：
Xiaodong Cao;Hung Tran
中科院分区：
文献类型：
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作者：
Xiaodong Cao;Hung Tran
本文主要研究四维闭流形。特别是，我们证明了在各种新的捏聚曲率条件下（例如，截面曲率不超过最小里奇特征值的5/6），那么该流形是确定的。如果限制到一个具有调和Weyl张量的度规，则在相同条件下，它一定是自对偶或反自对偶的。类似地，如果限制到爱因斯坦度量，那么它必须是具有Fubini-Study度量的复射影空间、圆球或它们的子空间。此外，我们还对具有正交形式和截面曲率上界的Einstein流形进行了分类。
In this paper, we study closed four-dimensional manifolds. In particular, we show that under various new pinching curvature conditions (for example, the sectional curvature is no more than 5/6 of the smallest Ricci eigenvalue) then the manifold is definite. If restricting to a metric with harmonic Weyl tensor, then it must be self-dual or anti-self-dual under the same conditions. Similarly, if restricting to an Einstein metric, then it must be either the complex projective space with its Fubini-Study metric, the round sphere or their quotients. Furthermore, we also classify Einstein manifolds with positive intersection form and an upper bound on the sectional curvature.