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arXiv · 1110.5994

On seven dimensional quaternionic contact solvable Lie groups

Diego Conti·Marisa Fernández·José A. Santisteban
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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 group.

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Diego Conti, Marisa Fernández, José A. Santisteban. 2012-01-24. On seven dimensional quaternionic contact solvable Lie groups. https://doi.org/10.1515/forum-2011-0128

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