Quaternionic contact manifolds with a closed fundamental 4-form

Abstract

We show that the fundamental 4-form on a quaternionic contact manifold of dimension at least eleven is closed if and only if the torsion endomorphism of the Biquard connection vanishes. This condition characterizes quaternionic contact structures which are locally qc homothetic to 3-Sasakian structures.

LaTeX 2e, 9 pages, no figures, final version to appear in Bull. London Math. Soc

References in corpus (2)

• Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem
• Explicit Quaternionic Contact Structures and Metrics with Special Holonomy

Cited by in corpus (6)

• Quaternionic Heisenberg groups as naturally reductive homogeneous spaces
• On seven dimensional quaternionic contact solvable Lie groups
• Explicit Quaternionic Contact Structures and Metrics with Special Holonomy
• Quaternionic Kaehler and Spin(7) metrics arising from quaternionic contact Einstein structures
• Intrinsic torsion in quaternionic contact geometry
• The Obata first eigenvalue theorems on a seven dimensional quaternionic contact manifold