Submaximally symmetric quaternion Hermitian structures

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Authors	KRUGLIKOV Boris WINTHER Henrik
Year of publication	2020
Type	Article in Periodical
Magazine / Source	International Journal of Mathematics
MU Faculty or unit	Faculty of Science
Citation
web	https://doi.org/10.1142/S0129167X20500846
Doi	https://doi.org/10.1142/S0129167X20500846
Keywords	Symmetry dimension; automorphism group; quaternion-Hermitian manifolds; the gap phenomenon; Wolf space; quaternion-Kahler structure
Description	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.
Related projects:	Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku