Hyper-ParaHermitian manifolds with torsion

Abstract

Necessary and sufficient conditions for the existence of a hyper-parahermitian connection with totally skew-symmetric torsion (HPKT-structure) are presented. It is shown that any HPKT-structure is locally generated by a real (potential) function. An invariant first order differential operator is defined on any almost hyper-paracomplex manifold showing that it is two-step nilpotent exactly when the almost hyper-paracomplex structure is integrable. A local HPKT-potential is expressed in terms of this operator. Examples of (locally) invariant HPKT-structures with closed as well as non-closed torsion 3-form on a class of (locally) homogeneous hyperparacomplex manifolds (some of them compact) are constructed.

latex, 20 pages, references clarified, final version, to appear in J. Goem. Phys

References in corpus (5)

• A Geometry for Non-Geometric String Backgrounds
• Potentials for hyper-Kahler metrics with torsion
• Para-Hermitian and Para-Quaternionic manifolds
• Classification of four-dimensional Lie algebras admitting a para-hypercomplex structure
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Cited by in corpus (6)

• A Unique Connection for Born Geometry
• On paraquaternionic submersions between paraquaternionic Kähler manifolds
• Homogeneous para-Kähler Einstein manifolds
• Compact complex surfaces with geometric structures related to split quaternions
• Geometry of Paraquaternionic Kahler manifolds with torsion
• Connections functorially attached to almost complex product structures