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

Boris Kruglikov; Henrik Winther

paper

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

arXiv:1512.07161

Abstract

For an almost complex structure $J$ in dimension 6 with nondegenerate Nijenhuis tensor $N_{J}$ , the automorphism group $G = A u t (J)$ 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-) Kähler and globally homogeneous. Moreover, we show that all examples with $dim A u t (J) = 9$ have semi-simple isotropy.