On the moment-angle manifolds of positive Ricci curvature (Q536623)

A moment angle manifold \(Z_P\) is constructed from a polyhedron \(P\) and a torus \(T\) acts freely on \(Z_P\) in a canonical fashion so \(Z_P/T=P\). The authors construct Riemannian metrics of positive Ricci curvature on some moment angle manifolds to examine the topological complexity of manifolds admitting a Riemannian metric of positive Ricci curvature. The main result of the article is: Theorem. Take an octahedron \(P\) obtained from a \(3\)-dimensional cube by cutting off small neighborhoods of two edges lying on skew-lines. The \(11\)-dimensional moment angle manifold \(Z_P\) admits a Riemannian metric of positive Ricci curvature. Although the authors also consider other moment-angle manifolds with metrics of positive Ricci curvature, the space in the theorem has a rather complicated topology. Its cohomology contains non-trivial Massey products and, thus, \(Z_P\) is a nonformal moment angle manifold.