Stability of Einstein metrics on symmetric spaces of compact type

@article{Schwahn2021StabilityOE,
  title={Stability of Einstein metrics on symmetric spaces of compact type},
  author={Paul Schwahn},
  journal={Annals of Global Analysis and Geometry},
  year={2021}
}
  • Paul Schwahn
  • Published 18 December 2020
  • Mathematics
  • Annals of Global Analysis and Geometry
<jats:p>We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces <jats:inline-formula><jats:alternatives><jats:tex-math>$${\text {SU}}(n)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>SU</mml:mtext> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math></jats… 
View PDF on arXiv
7 Citations
Background Citations
2

7 Citations

Stability of the Non–Symmetric Space E 7 / PSO (8)
We prove that the normal metric on the homogeneous space E 7 / PSO (8) is stable with respect to the Einstein-Hilbert action, thereby exhibiting the first known example of a non-symmetric metric of…
Stability of the Non-Symmetric Space $E_7/\mathrm{PSO}(8)$
We prove that the normal metric on the homogeneous space E7/PSO(8) is stable with respect to the Einstein-Hilbert action, thereby exhibiting the first known example of a non-symmetric metric of…
Coindex and rigidity of Einstein metrics on homogeneous Gray manifolds
Any 6-dimensional strict nearly K¨ahler manifold is Einstein with positive scalar curvature. We compute the coindex of the metric with respect to the Einstein-Hilbert functional on each of the…
Homogeneous Einstein metrics and local maxima of the Hilbert action
The stability of standard homogeneous Einstein manifolds
Back in 1985, Wang and Ziller obtained a complete classification of all homogeneous spaces of compact simple Lie groups on which the standard or Killing metric is Einstein. The list consists, beyond…
On the stability of homogeneous Einstein manifolds
. Let g be a G -invariant Einstein metric on a compact homogeneous space M = G/K . We use a formula for the Lichnerowicz Laplacian of g at G -invariant TT tensors to study the stability type of g as…
Rigidity of $SU_n$-type symmetric spaces
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…

References

SHOWING 1-10 OF 14 REFERENCES
On the Lichnerowicz Laplace operator and its application to stability of spacetimes
  • Mathematics
  • 2013
Le Spectre d'une Variete Riemannienne
Propagateurs et commutateurs en relativité générale
© Publications mathématiques de l’I.H.É.S., 1961, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…
Radon transforms and spectral rigidity on the complex quadrics and the real Grassmannians of rank two.
Representation Theory: A First Course
This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras. Following an introduction to representation…
Rigidity and stability of Einstein metrics---the case of compact symmetric spaces
Let M be a compact connected manifold of d i m M ^ 2 and g an Einstein metric on M. If (M, g) is the standard sphere, then all Einstein metrics £' on M near g are of constant sectional curvature, and…
Rigidity and infinitesimal deformability of Einstein metrics
Let (M,g) be a compact Einstein manifold. If all Einstein metrics on M near g are homothetic to <§ , then the Einstein metric g is said to be rigid. The first result concerning the rigidity of…
Bohm and Einstein-Sasaki metrics, black holes, and cosmological event horizons
We study physical applications of the Bohm metrics, which are infinite sequences of inhomogeneous Einstein metrics on spheres and products of spheres of dimension 5 <= d <= 9. We prove that all the…
Gaussian densities and stability for some Ricci solitons
In this announcement, we exhibit the second variation of Perelman's $\lambda$ and $\nu$ functionals for the Ricci flow, and investigate the linear stability of examples. We also define the "central…
Linear stability of Perelman's $ν$-entropy on symmetric spaces of compact type
Following Cao-Hamilton-Ilmanen, in this paper we study the linear stability of Perelman's $\nu$-entropy on Einstein manifolds with positive Ricci curvature. We observe the equivalence between the…
...
...