2011/08/18 by Yu Li, Li Yu, Yu, Li
Mathematics · #51H30 #53C25 #57N16 #57S17 #57S25 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #math.AT #math.DG #math.GT #msc:51H30 #msc:53C25 #msc:57N16 #msc:57S17 #msc:57S25
paper · pdf · doi:10.48550/arxiv.1108.3782
The main results in this paper have been superseded by arXiv:1111.2174
openalex publication_date 2011/08/18 · arxiv created 2011/11/10 · arxiv updated 2011/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that all the small covers which are infra-nilmanifolds are exactly real Bott manifolds. This implies that any small cover which admits a flat Riemannian metric must be a real Bott manifold. In addition, we will study small covers which admit Riemannian metrics with positive or nonnegative Ricci curvature or sectional curvature. We will see that these geometric conditions put very strong restrictions on the topology of the small covers and the combinatorial structure of the underlying simple polytopes. Similar geometric problems are also studied for the real moment-angle complex of an arbitrary simple polytope.