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


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.