Small Cover, infra-solvmanifold and curvature

Details Small Cover, infra-solvmanifold and curvature Small Cover, infra-solvmanifold and curvature

2011-11-09

arxiv.org/abs/1111.2174v1

Mathematics

Geometric Topology

19 pages, no figure

Scientific paper

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 equivalent 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.

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