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arXiv · 2011.11965

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

Uwe Semmelmann·Changliang Wang·M. Y. -K. Wang
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Abstract

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.

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Uwe Semmelmann, Changliang Wang, M. Y. -K. Wang. 2020-11-24. Linear Instability of Sasaki Einstein and nearly parallel ${\rm G}_2$ manifolds. https://arxiv.org/abs/2011.11965

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