International Journal of Mathematics ( IF 0.604 ) Pub Date : 2020-09-03 , DOI: 10.1142/s0129167x20500846 Boris Kruglikov; Henrik Winther
We consider and resolve the gap problem for almost quaternion-Hermitian structures, i.e. we determine the maximal and submaximal symmetry dimensions, both for Lie algebras and Lie groups, in the class of almost quaternion-Hermitian manifolds. We classify all structures with such symmetry dimensions. Geometric properties of the submaximally symmetric spaces are studied, in particular, we identify locally conformally quaternion-Kähler structures as well as quaternion-Kähler with torsion.