Almost complex structures in 6D with nondegenerate Nijenhuis tensors and large symmetry groups

Boris Kruglikov; Henrik Winther

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arXiv · 1512.07161

Almost complex structures in 6D with nondegenerate Nijenhuis tensors and large symmetry groups

Boris Kruglikov·Henrik Winther

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Abstract

For an almost complex structure $J$ in dimension 6 with nondegenerate Nijenhuis tensor $N_J$, the automorphism group $G=Aut(J)$ of maximal dimension is the exceptional Lie group $G_2$. In this paper we establish that the sub-maximal dimension of automorphism groups of almost complex structures with nondegenerate $N_J$, i.e. the largest realizable dimension that is less than 14, is $\dim G=10$. Next we prove that only 3 spaces realize this, and all of them are strictly nearly (pseudo-) K\"ahler and globally homogeneous. Moreover, we show that all examples with $\dim Aut(J)=9$ have semi-simple isotropy.

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Boris Kruglikov, Henrik Winther. 2015-12-22. Almost complex structures in 6D with nondegenerate Nijenhuis tensors and large symmetry groups. https://arxiv.org/abs/1512.07161

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