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Moment-angle manifolds with positiv Ricci curvature which correspond to a 3-cube. (English. Russian original) Zbl 1220.53047

Russ. Math. Surv. 66, No. 2, 437-438 (2011); translation from Usp. Mat. Nauk 66, No. 2, 233-234 (2011).
Summary: An interesting question in Riemannian geometry concerns the topological complexity of manifolds admitting Riemannian metrics with positive Ricci curvature. In [Ya. V. Bazaĭkin and I. V. Matvienko, Sib. Math. J. 52, No. 1, 11–22 (2011); translation from Sib. Mat. Zh. 52, No. 1, 15–29 (2011; Zbl 1220.53041)] we put forward a method for constructing Riemannian metrics with positive Ricci curvature on certain moment-angle manifolds. In particular, we gave an example of a non-formal moment-angle manifold with positive Ricci curvature. In this note, we describe all moment-angle manifolds corresponding to a 3-cube with a truncated system of vertices and faces, on which, using the method in [loc. cit.], we can construct Riemannian metrics with positive Ricci curvature.

MSC:

53C20 Global Riemannian geometry, including pinching
52B10 Three-dimensional polytopes

Citations:

Zbl 1220.53041
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