Submaximally Symmetric Quaternion Hermitian Structures
Differential Geometry
2020-08-19 v2
Abstract
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-K\"ahler structures as well as quaternion-K\"ahler with torsion.
Cite
@article{arxiv.1812.11229,
title = {Submaximally Symmetric Quaternion Hermitian Structures},
author = {Boris Kruglikov and Henrik Winther},
journal= {arXiv preprint arXiv:1812.11229},
year = {2020}
}
Comments
final version: minor corrections