2017
DOI: 10.1142/s0129167x17500057
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Stability of Riemannian manifolds with Killing spinors

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Cited by 15 publications
(28 citation statements)
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“…A particularly interesting and important special case is that of regular Sasaki-Einstein metrics, which exist on certain special circle bundles over Kähler Einstein manifolds. By combining Corollary 6.1 of [Wan17] and an observation after Example 2.3 in [CHI04], we show that if the second Betti number b 2 of the Kähler Einstein base is strictly greater than 1 then the regular Sasaki-Einstein manifold is unstable. This in particular includes the instability result in Corollary 6.2 of [Wan17].…”
Section: Introductionmentioning
confidence: 69%
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“…A particularly interesting and important special case is that of regular Sasaki-Einstein metrics, which exist on certain special circle bundles over Kähler Einstein manifolds. By combining Corollary 6.1 of [Wan17] and an observation after Example 2.3 in [CHI04], we show that if the second Betti number b 2 of the Kähler Einstein base is strictly greater than 1 then the regular Sasaki-Einstein manifold is unstable. This in particular includes the instability result in Corollary 6.2 of [Wan17].…”
Section: Introductionmentioning
confidence: 69%
“…By combining Corollary 6.1 of [Wan17] and an observation after Example 2.3 in [CHI04], we show that if the second Betti number b 2 of the Kähler Einstein base is strictly greater than 1 then the regular Sasaki-Einstein manifold is unstable. This in particular includes the instability result in Corollary 6.2 of [Wan17]. Thus for the stability of regular Sasaki-Einstein manifolds, we are reduced to those spaces with Fano Kähler Einstein bases with b 2 = 1.…”
Section: Introductionmentioning
confidence: 69%
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“…Kröncke [16] and the second author [24], the Einstein metrics (with negative scalar curvature) are also linearly stable.…”
mentioning
confidence: 97%
“…In [25], we showed that all the homogeneous nearly Kähler 6-manifolds other than the isotropy irreducible space G 2 /SU(3) ≈ S 6 are linearly unstable. Theorem 1.1 provides some additional information for these cases.…”
mentioning
confidence: 99%