Kähler-Ricci solitons on homogeneous toric bundles

By F. Podestà, A. Spiro. 2006

53 citations recorded by the source corpus.

Abstract We deal with homogeneous toric bundles M over generalized flag manifolds GC /P, where G is a compact semisimple Lie group and P a parabolic subgroup. Using symplectic data, we provide a simple characterization of the homogeneous toric bundles M which are Fano; we then show that a homogeneous toric bundle M admits a Kähler-Ricci solitonic metric if and only if it is Fano.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c9943c2e1fac7fbc8d7b0ef3fd9f1e33e26afd75

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Kähler–Einstein metrics along the smooth continuity method (2015, background): “These are the homogeneous toric bundles studied by Podesta-Spiro [37], who showed that all such Fano manifolds admit a Kähler-Ricci soliton.”
K-stability of Fano spherical varieties (2016, methodology): “roup compactiﬁcations in [Del15, Del] can be adapted to provide another proof of the criterion for Kähler-Ricci solitons on the same manifolds. Similarly, Wang-Zhu type methods (as used in [WZ04] and [PS10]), together with some results proved for horospherical manifolds in the present paper, could b”
On Ricci solitons of cohomogeneity one (2008, methodology): “4, the integral (4.24 )v anishes forsomechoiceof κ1).Inthecaseofcompactshrinkingsolitonswithnoblowing-downthese examples are included in those found by different methods in [ 36 ].”