Hyper-ParaHermitian manifolds with torsion
arXiv:math/0405585 · doi:10.1016/j.geomphys.2005.04.012
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.
arXiv commentlatex, 20 pages, references clarified, final version, to appear in J. Goem. Phys
References in corpus (11)
- A Geometry for Non-Geometric String Backgrounds
- Twistor spaces for HKT manifolds
- Geometry of Hyper-Kähler Connections with Torsion
- The Geometry of (Super) Conformal Quantum Mechanics
- Kleinian Geometry and the N=2 Superstring
- Actions For (2,1) Sigma-Models and Strings
- Potentials for hyper-Kahler metrics with torsion
- Para-Hermitian and Para-Quaternionic manifolds
- Hyper-complex four-manifolds from the Tzitzéica equation
- Complex product structures on some simple Lie groups
- Classification of four-dimensional Lie algebras admitting a para-hypercomplex structure
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