The canonical Einstein metric on G2 is dynamically unstable under the Ricci flow

Hall, Stuart James

doi:10.1112/blms.12238

Cited by 5 publications

(2 citation statements)

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“…Finally, we note that the bi-invariant metric on the compact Lie group G 2 is known to admit infinitesimal solitonic deformations [4]. In [10], the second author demonstrated that there exist deformations that are not integrable to second order and hence the Einstein metric is dynamically unstable. It would be interesting to extend this analysis to characterise precisely which solitonic deformations are not integrable.…”

Section: 2mentioning

confidence: 90%

Rigidity of $SU_n$-type symmetric spaces

Batat¹,

Hall²,

Murphy³

et al. 2021

Preprint

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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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Section: 2mentioning

confidence: 90%

Rigidity of $SU_n$-type symmetric spaces

Batat¹,

Hall²,

Murphy³

et al. 2021

Preprint

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“…Since the operator C is non-negative we get that σ " 0 for λ " 1, so H 1 " 0. Further on the algebraic constraints on σ lead to C ρbπ 1 σ " pλ ´4qpλ ´2qσ according to (15). Since C ρbπ 1 is non-negative σ " 0 for λ " 3 and σ is sup2q-invariant w.r.t.…”

Section: Infinitesimal Einstein and G 2 Deformationsmentioning

confidence: 99%

The $G_2$ geometry of $3$-Sasaki structures

Nagy,

Semmelmann

2021

Preprint

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We initiate a systematic study of the deformation theory of the second Einstein metric g 1{ ? 5 respectively the proper nearly G 2 structure ϕ 1{ ? 5 of a 3-Sasaki manifold pM 7 , gq. We show that infinitesimal Einstein deformations for g 1{ ? 5 coincide with infinitesimal G 2 deformations for ϕ 1{ ? 5 . The latter are showed to be parametrised by eigenfunctions of the basic Laplacian of g, with eigenvalue twice the Einstein constant of the 4-dimensional base orbifold, via an explicit differential operator. In terms of this parametrisation we determine those infinitesimal G 2 deformations which are unobstructed to second order.

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