On the linear stability of nearly Kähler 6-manifolds

Semmelmann, Uwe; Wang, Changliang; Wang, M. Y.-K.

doi:10.1007/s10455-019-09686-5

Cited by 13 publications

(16 citation statements)

References 21 publications

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“…In passing, we observe that there are fewer different fundamental weights than shown in this diagram for n ≤ 4. The classification of all possible critical representations of the Lie algebras sl(n + 1, C) with n ≥ 1 follows from the lower linear estimate (17), the inequality…”

Section: Critical Representations Of Simple Lie Algebrasmentioning

confidence: 99%

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Stability of Compact Symmetric Spaces

Semmelmann

Weingart

2022

J Geom Anal

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In this article, we study the stability problem for the Einstein–Hilbert functional on compact symmetric spaces following and completing the seminal work of Koiso on the subject. We classify in detail the irreducible representations of simple Lie algebras with Casimir eigenvalue less than the Casimir eigenvalue of the adjoint representation and use this information to prove the stability of the Einstein metrics on both the quaternionic and Cayley projective plane. Moreover, we prove that the Einstein metrics on quaternionic Grassmannians different from projective spaces are unstable.

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Section: Critical Representations Of Simple Lie Algebrasmentioning

confidence: 99%

“…Besides Koiso's notion, there actually exists a weaker notion of stability of Einstein metrics, the so-called S-linear stability (cf. [17,18]), which allows for the presence of infinitesimal deformations. More precisely an Einstein metric is called S-linearly stable, if S is non-positive on the space of tt-tensors.…”

Section: Introductionmentioning

confidence: 99%

Stability of Compact Symmetric Spaces

Semmelmann

Weingart

2022

J Geom Anal

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“…Linear stability. The following theorem about the linear stability of nearly Kähler manifolds is known by Semmelmann, Wang, and Wang [19].…”

Section: 1mentioning

confidence: 99%

Rarita-Schwinger fields on nearly Kähler manifolds

Ohno,

Tomihisa

2021

Preprint

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We study Rarita-Schwinger fields on 6-dimensional compact strict nearly Kähler manifolds. In order to investigate them, we clarify the relationship between some differential operators for the Hermitian connection and the Levi-Civita connection. As a result, we show that the space of the Rarita-Schwinger fields coincides with the space of the harmonic 3-forms. Applying the same technique to a deformation theory, we also find that the space of the infinitesimal deformations of Killing spinors coincides with the direct sum of a certain eigenspace of the Laplace operator and the space of the Killing spinors.

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“…Besides Koiso's notion there actually exists a weaker notion of stability of Einstein metrics, the so-called S-linear stability (cf. [16], [15]), which allows for the presence of infinitesimal deformations. More precisely an Einstein metric is called S-linearly stable, if S ′′ is non-positive on the space of tt-tensors.…”

Section: Introductionmentioning

confidence: 99%

Stability of Compact Symmetric Spaces

Semmelmann¹,

Weingart²

2020

Preprint

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In this article we study the stability problem for the Einstein-Hilbert functional on compact symmetric spaces following and completing the seminal work of Koiso on the subject. We classify in detail the irreducible representations of simple Lie algebras with Casimir eigenvalue less than the Casimir eigenvalue of the adjoint representation, and use this information to prove the stability of the Einstein metrics on both the quaternionic and Cayley projective plane. Moreover we prove that the Einstein metrics on quaternionic Grassmannians different from projective spaces are unstable.

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On the linear stability of nearly Kähler 6-manifolds

Abstract: We show that a strict, nearly Kähler 6-manifold with either second or third Betti number nonzero is linearly unstable with respect to the ν-entropy of Perelman and hence is dynamically unstable for the Ricci flow.

Cited by 13 publications

References 21 publications

Stability of Compact Symmetric Spaces

Stability of Compact Symmetric Spaces

Rarita-Schwinger fields on nearly Kähler manifolds

Stability of Compact Symmetric Spaces

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