Submaximally symmetric quaternion Hermitian structures
|Year of publication
|Article in Periodical
|Magazine / Source
|International Journal of Mathematics
|MU Faculty or unit
|Symmetry dimension; automorphism group; quaternion-Hermitian manifolds; the gap phenomenon; Wolf space; quaternion-Kahler structure
|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-Kahler structures as well as quaternion-Kahler with torsion.