Linear instability of Sasaki Einstein and nearly parallel G2 manifolds

Abstract

In this paper, we study the stability problem for the Einstein metrics on Sasaki Einstein and on complete nearly parallel [Formula: see text] manifolds. In the Sasaki case we show linear instability if the second Betti number is positive. Similarly, we prove that nearly parallel [Formula: see text] manifolds with positive third Betti number are linearly unstable. Moreover, we prove linear instability for the Berger space [Formula: see text] which is a [Formula: see text]-dimensional homology sphere with a proper nearly parallel [Formula: see text] structure.