On seven dimensional quaternionic contact solvable Lie groups

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.

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

References in corpus (6)

• Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem
• Quaternionic contact manifolds with a closed fundamental 4-form
• Quaternionic Kaehler and Spin(7) metrics arising from quaternionic contact Einstein structures
• Quaternionic-contact hypersurfaces
• On the twistor space of a quaternionic contact manifold
• The twistor space of a quaternionic contact manifold

Cited by in corpus (3)

• Quaternionic contact Einstein manifolds
• Solvable groups and a shear construction
• Intrinsic torsion in quaternionic contact geometry