Infinitesimal Einstein Deformations of Nearly Kähler Metrics

Abstract

It is well-known that every 6-dimensional strictly nearly Kähler manifold $(M,g,J)$ is Einstein with positive scalar curvature $scal>0$. Moreover, one can show that the space $E$ of co-closed primitive (1,1)-forms on $M$ is stable under the Laplace operator $\Delta$. Let $E(a)$ denote the $a$-eigenspace of the restriction of $\Delta$ to $E$. If $M$ is compact, we prove that the moduli space of infinitesimal Einstein deformations of the nearly Kähler metric $g$ is naturally isomorphic to the direct sum $E(scal/15)\oplus E(scal/5)\oplus E(2scal/5)$. It is known that the last summand is itself isomorphic with the moduli space of infinitesimal nearly Kähler deformations.

References in corpus (1)

• The Hermitian Laplace Operator on Nearly Kähler Manifolds

Cited by in corpus (3)

• The Hermitian Laplace Operator on Nearly Kähler Manifolds
• Left-invariant Einstein metrics on $S^3\times S^3$
• Generalized vector cross products and Killing forms on negatively curved manifolds