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

2015/12/22 by Boris Kruglikov, Kruglikov, Boris, Henrik Winther +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1512.07161

openalex publication_date 2015/12/22 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28

Abstract

For an almost complex structure J in dimension 6 with nondegenerate\nNijenhuis tensor N_J, the automorphism group G=Aut(J) of maximal dimension\nis the exceptional Lie group G₂. In this paper we establish that the\nsub-maximal dimension of automorphism groups of almost complex structures with\nnondegenerate N_J, i.e. the largest realizable dimension that is less than\n14, is \dim G=10. Next we prove that only 3 spaces realize this, and all of\nthem are strictly nearly (pseudo-) K "ahler and globally homogeneous. Moreover,\nwe show that all examples with \dim Aut(J)=9 have semi-simple isotropy.\n

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