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 $G_{2}$ 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 $S O (5) / S O (3)_{i r r}$ which is a $7$ -dimensional homology sphere with a proper nearly parallel $G_{2}$ structure.

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

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

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Linear Instability of Sasaki Einstein and nearly parallel G2G2​ manifolds

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Linear Instability of Sasaki Einstein and nearly parallel G2G2​ manifolds

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

讲解博客

AI智能校验

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

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AI智能校验