arXiv subjects

M. Y. -K. Wang

Publications and source records attributed to M. Y. -K. Wang.

3 recordsLinked to original sources

arXiv2020

Linear Instability of Sasaki Einstein and nearly parallel ${\rm G}_2$ manifolds

In this article we study the stability problem for the Einstein metrics on Sasaki Einstein and on complete nearly parallel ${\rm G}_2$ manifolds. In the Sasaki case we show linear instability if the second Betti number is positive. Similarly we prove that nearly parallel $\rm G_2$ manifolds with positive third Betti number are linearly unstable. Moreover, we prove linear instability for the Berger space ${\rm SO}(5)/{\rm SO}(3)_{irr} $ which is a $7$-dimensional homology sphere with a proper nearly parallel ${\rm G}_2$ structure.

math.DG↗

arXiv2019

On the linear stability of nearly-Kähler $6$-manifolds

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.

math.DG↗

arXiv2018

Instability of some Riemannian manifolds with real Killing spinors

We prove the instability of some families of Riemannian manifolds with non-trivial real Killing spinors. These include the invariant Einstein metrics on the Aloff-Wallach spaces $N_{k, l}={\rm SU}(3)/i_{k, l}(S^{1})$ (which are all nearly ${\rm G}_2$ except $N_{1,0}$), and Sasaki Einstein circle bundles over certain irreducible Hermitian symmetric spaces. We also prove the instability of most of the simply connected non-symmetric compact homogeneous Einstein spaces of dimensions $5, 6, $ and $7$, including the strict nearly Kähler ones (except ${\rm G}_2/{\rm SU}(3)$).

math.DG↗