SMALL COVER, INFRA-SOLVMANIFOLD AND CURVATURE
SMALL COVER, INFRA-SOLVMANIFOLD AND CURVATURE
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DOI：
10.1515/forum-2013-0084
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发表时间：
2011-11
期刊：
影响因子：
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通讯作者：
S. Kuroki;M. Masuda;Li Yu
中科院分区：
文献类型：
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作者：
S. Kuroki;M. Masuda;Li Yu
结果表明，简单多面体上的小覆盖（分别为实矩角流形）当且仅当它与实数 Bott 流形（分别为平环面）微分同胚时，才是下求解流形。此外，我们获得了小覆盖与真实 Bott 流形同胚的几个等效条件。此外，我们在 Ricci 或截面曲率的某些条件下研究小覆盖和实矩角流形上的黎曼度量。我们将看到这些曲率条件对相应的小覆盖和实矩角流形的拓扑以及底层简单多面体的组合结构施加了非常强的限制。
It is shown that a small cover (resp. real moment-angle manifold) over a simple polytope is an infra-solvmanifold if and only if it is diffeomorphic to a real Bott manifold (resp. flat torus). Moreover, we obtain several equiva- lent conditions for a small cover being homeomorphic to a real Bott manifold. In addition, we study Riemannian metrics on small covers and real moment- angle manifolds with certain conditions on the Ricci or sectional curvature. We will see that these curvature conditions put very strong restrictions on the topology of the corresponding small covers and real moment-angle manifolds and the combinatorial structure of the underlying simple polytopes.