Expanding Kähler–Ricci solitons coming out of Kähler cones

Conlon, Ronan J.; Deruelle, Alix

doi:10.4310/jdg/1589853627

Cited by 12 publications

(17 citation statements)

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“…Let Ric T denote the Ricci curvature of the local orbit space of F ξ . Then again elementary computations show (5) Ric g = Ric T − 2g T + 2mη ⊗ η and that the condition of η-Einstein metric is equivalent to…”

Section: Theorem 22 ([17]mentioning

confidence: 99%

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Irregular Eguchi-Hanson type metrics and their soliton analogues

Futaki¹

2020

Preprint

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We verify the extension to the zero section of momentum construction of Kähler-Einstein metrics and Kähler-Ricci solitons on the total space of positive rational powers of the canonical line bundle of toric Fano manifolds with possibly irregular Sasaki-Einstein metrics. More precisely, we show the metric extends to the associated unit circle bundle as a transversely Kähler-Einstein (Sasakian eta-Einstein) metric squashed in the Reeb flow direction.

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Section: Theorem 22 ([17]mentioning

confidence: 99%

“…In this soliton case we also use Hwang-Singer's momentum construction while existence results using gluing method have been known by [24], [5] for expanding solitons and by [6] for steady solitons. For uniqueness there are works by [7], [23] and [3].…”

Section: Introductionmentioning

confidence: 99%

Irregular Eguchi-Hanson type metrics and their soliton analogues

Futaki¹

2020

Preprint

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“…Indeed, Schulze-Simon [51] obtained gradient expanding solitons out of the asymptotic cones at infinity of solutions to the Ricci flow on complete noncompact Riemannian manifolds with bounded and non-negative curvature operator and positive asymptotic volume ratio. See also more recent work [32,27].…”

Section: Introductionmentioning

confidence: 98%

Curvature Estimates for Four-Dimensional Gradient Steady Ricci Solitons

Cao

Cui

2019

J Geom Anal

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“…Explicit examples of Kähler-Ricci solitons were given in [C2], and those are both expanding and U (n)-invariant. Other early and more recent examples appear in [K,C1,CV,G,PTV,FIK,Y,FW,CD]. Among metrics on homogeneous manifolds, there is a well-known correspondence between left-invariant Einstein metrics on solvable Lie groups and homogeneous Ricci solitons on their nilradicals [La1].…”

Section: Introductionmentioning

confidence: 99%

Cohomogeneity one Kähler-Ricci solitons under a Heisenberg group action and related metrics

Maschler¹,

Ream²

2020

Preprint

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We show that integrability of an almost complex structure in complex dimension m is equivalent, in the presence of an almost hermitian metric, to m(m − 1) equations involving what we call shear operators. Inspired by this, we give an ansatz for Kähler metrics in dimension m > 1, for which only m − 1 of these shear equations are non-trivial. The equations for gradient Kähler-Ricci solitons in this ansatz are frame dependent PDEs, which specialize to ODEs under extra assumptions. Metrics solving the latter system include a restricted class of cohomogeneity one metrics, and we find among them complete expanding gradient Kähler-Ricci solitons under the action of the (2m − 1)-dimensional Heisenberg group, and some incomplete steady solitons. In another special case of the ansatz we present, for m = 2, a class of complete metrics of a more general type which we call gradient Kähler-Ricci skew-solitons, which are cohomogeneity one under the Euclidean plane group action. This paper continues research started in [MR,AM2].

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Expanding Kähler–Ricci solitons coming out of Kähler cones

Cited by 12 publications

References 0 publications

Irregular Eguchi-Hanson type metrics and their soliton analogues

Irregular Eguchi-Hanson type metrics and their soliton analogues

Curvature Estimates for Four-Dimensional Gradient Steady Ricci Solitons

Cohomogeneity one Kähler-Ricci solitons under a Heisenberg group action and related metrics

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