# Almost complex structures in 6D with non-degenerate Nijenhuis tensors and large symmetry groups

Research paper by B. S. Kruglikov, H. Winther

Indexed on: 22 May '16Published on: 21 May '16Published in: Annals of Global Analysis and Geometry

#### Abstract

For an almost complex structure J in dimension 6 with non-degenerate Nijenhuis tensor $$N_J$$, the automorphism group $$G=\mathop {\mathrm{Aut}}\nolimits (J)$$ 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 non-degenerate $$N_J$$, i.e. the largest realizable dimension that is less than 14, is $$\dim G=10$$. Next, we prove that only three spaces realize this, and all of them are strictly nearly (pseudo-) Kähler and globally homogeneous. Moreover, we show that all examples with $$\dim \mathop {\mathrm{Aut}}\nolimits (J)=9$$ have semi-simple isotropy.