On seven dimensional quaternionic contact solvable Lie groups

Details On seven dimensional quaternionic contact solvable Lie groups On seven dimensional quaternionic contact solvable Lie groups

2011-10-27

arxiv.org/abs/1110.5994v2

Mathematics

Differential Geometry

23 pages, v2: typos corrected. To appear in Forum Math

Scientific paper

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.

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