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| Ricci Positive Metrics on the Moment-Angle Manifolds |
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Citation： |
Liman CHEN,Feifei FAN.Ricci Positive Metrics on the Moment-Angle Manifolds[J].Chinese Annals of Mathematics B,2019,40(3):469~480 |
| Page view： 847
Net amount： 563 |
Authors： |
Liman CHEN; Feifei FAN |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11471167, 11571186, 11701411, 11801580). |
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| Abstract： |
In this paper, the authors consider the problem of which
(generalized) moment-angle manifolds admit Ricci positive metrics.
For a simple polytope $P$, the authors can cut off one vertex $v$ of
$P$ to get another simple polytope $P_{v}$, and prove that if the
generalized moment-angle manifold corresponding to $P$ admits a
Ricci positive metric, the generalized moment-angle manifold
corresponding to $P_{v}$ also admits a Ricci positive metric. For a
special class of polytope called Fano polytopes, the authors prove
that the moment-angle manifolds corresponding to Fano polytopes
admit Ricci positive metrics. Finally some conjectures on this
problem are given. |
Keywords： |
Moment-Angle manifolds, Simple polytope, Cutting off face, PositiveRicci curvature, Fano polytope |
Classification： |
22E46, 53C30 |
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