Rigidity and Infinitesimal Deformability of Ricci Solitons

Kröncke, Klaus

doi:10.1007/s12220-015-9608-4

Cited by 10 publications

(18 citation statements)

References 8 publications

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“…which implies that v h,K is a constant. Then, the operator N in (26), related to the second variation formula, reduces to…”

Section: ∇G : Omentioning

confidence: 99%

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The Stability of Generalized Ricci Solitons

Lee¹

2022

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In [12,28], it was shown that the generalized Ricci flow is the gradient flow of a functional λ generalizing Perelman's λ functional for Ricci flow. In this work, we further computed the second variation formula and proved that a Bismut-flat, Einstein manifold is linearly stable under some curvature assumptions. In the last part of this paper, I proved that the dynamical stability and the linear stability are equivalent on a steady gradient generalized Ricci soliton (g, H, f ). This generalizes the results in [15,22,25,31,33].

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“…which implies that v h,K is a constant. Then, the operator N in (26), related to the second variation formula, reduces to…”

Section: ∇G : Omentioning

confidence: 99%

“…Lemma 4.2. Let N be the second variation operator on a steady gradient generalized Ricci soliton (M, g, H, f ) defined in (26). Then,…”

Section: Introductionmentioning

confidence: 99%

The Stability of Generalized Ricci Solitons

Lee¹

2022

Preprint

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“…Munteanu [6] discussed the curvature behavior of four dimensional shrinking gradient Ricci solitons. Kroencke [7] showed that though complex projective spaces of even complex dimension have infinitesimal solitonic deformations, they are rigid as Ricci solitons. Catino et al [8] provided some necessary integrability conditions for the existence of gradient Ricci solitons in conformal Einstein manifolds.…”

Section: Introductionmentioning

confidence: 99%

Kinematic Description of Ricci Solitons in Fluid Spacetimes

Sheikh

2017

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“…Theorem C (Kröncke, [18]). The Fubini-Study metric on CP 2n is isolated in the moduli space of Ricci solitons.…”

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confidence: 99%

“…Theorem 5.3 (Kröncke, Theorem 5.7 in [18]). Let (M, g) be an Einstein metric with Einstein constant λ > 0 and let v ∈ V −2λ .…”

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confidence: 99%

Rigidity of $SU_n$-type symmetric spaces

Batat¹,

Hall²,

Murphy³

et al. 2021

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We prove that the bi-invariant Einstein metric on SU2n+1 is isolated in the moduli space of Einstein metrics, even though it admits infinitesimal deformations. This gives a non-Kähler, non-product example of this phenomenon adding to the famous example of CP 2n × CP 1 found by Koiso. We apply our methods to derive similar solitonic rigidity results for the Kähler-Einstein metrics on 'odd' Grassmannians. We also make explicit a connection between non-integrable deformations and the dynamical instability of metrics under Ricci flow.

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Rigidity and Infinitesimal Deformability of Ricci Solitons

Cited by 10 publications

References 8 publications

The Stability of Generalized Ricci Solitons

The Stability of Generalized Ricci Solitons

Kinematic Description of Ricci Solitons in Fluid Spacetimes

Rigidity of $SU_n$-type symmetric spaces

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