Infinitesimal Einstein Deformations of Nearly Kähler Metrics

Details Infinitesimal Einstein Deformations of Nearly Kähler Metrics Infinitesimal Einstein Deformations of Nearly Kähler Metrics

2007-02-15

arxiv.org/abs/math/0702455v2

Trans. Amer. Math. Soc. 363, 3057-3069 (2011)

Mathematics

Differential Geometry

Scientific paper

10.1090/S0002-9947-2011-05064-6

It is well-known that every 6-dimensional strictly nearly K\"{a}hler 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 K\"{a}hler 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 K\"{a}hler deformations.

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