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

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

paper

Linear Instability of Sasaki Einstein and nearly parallel $G_{2}$ manifolds

arXiv:2011.11965

Abstract

In this article we study the stability problem for the Einstein metrics on Sasaki Einstein and on complete nearly parallel $G_{2}$ manifolds. In the Sasaki case we show linear instability if the second Betti number is positive. Similarly we prove that nearly parallel $G_{2}$ manifolds with positive third Betti number are linearly unstable. Moreover, we prove linear instability for the Berger space $SO (5) / SO (3)_{i r r}$ which is a $7$ -dimensional homology sphere with a proper nearly parallel $G_{2}$ structure.

13 pages

Linear Instability of Sasaki Einstein and nearly parallel G2​ manifolds

Abstract

References in corpus (2)

Linear Instability of Sasaki Einstein and nearly parallel $G_{2}$ manifolds