We answer in the affirmative a question posed by Ivanov and Vassilev on the existence of a seven-dimensional quaternionic contact manifold with closed fundamental 4-form and non-vanishing torsion endomorphism. Moreover, we show an approach to the classification of seven-dimensional solvable Lie groups having an integrable left invariant quaternionic contact structure. In particular, we prove that the unique seven-dimensional nilpotent Lie group admitting such a structure is the quaternionic Heisenberg group
Conti, D., Fernández, M., Santisteban, J. (2014). On seven-dimensional quaternionic contact solvable Lie groups. FORUM MATHEMATICUM, 26(2), 547-576 [10.1515/forum-2011-0128].
On seven-dimensional quaternionic contact solvable Lie groups
CONTI, DIEGO;
2014
Abstract
We answer in the affirmative a question posed by Ivanov and Vassilev on the existence of a seven-dimensional quaternionic contact manifold with closed fundamental 4-form and non-vanishing torsion endomorphism. Moreover, we show an approach to the classification of seven-dimensional solvable Lie groups having an integrable left invariant quaternionic contact structure. In particular, we prove that the unique seven-dimensional nilpotent Lie group admitting such a structure is the quaternionic Heisenberg groupFile | Dimensione | Formato | |
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