Potential one-forms for hyperkähler structures with torsion

Abstract

It is shown that an HKT-space with closed parallel potential 1-form has $D(2,1;-1)$-symmetry. Every locally conformally hyperkähler manifold generates this type of geometry. The HKT-spaces with closed parallel potential 1-form arising in this way are characterized by their symmetries and an inhomogeneous cubic condition on their torsion.

16 pages, Latex, no figures

References in corpus (6)

• HKT and OKT Geometries on Soliton Black Hole Moduli Spaces
• Geometry of Hyper-Kähler Connections with Torsion
• The Geometry of (Super) Conformal Quantum Mechanics
• Superconformal Multi-Black Hole Quantum Mechanics
• Geometry of Quaternionic Kähler connections with torsion
• Superconformal symmetry and hyperKaehler manifolds with torsion

Cited by in corpus (3)

• Twisting Hermitian and hypercomplex geometries
• Reduction of Vaisman structures in complex and quaternionic geometry
• Heterotic geometry without isometries