Hyper-ParaHermitian manifolds with torsion
摘要
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.
引用
@article{arxiv.math/0405585,
title = {Hyper-ParaHermitian manifolds with torsion},
author = {Stefan Ivanov and Vasil Tsanov and Simeon Zamkovoy},
journal= {arXiv preprint arXiv:math/0405585},
year = {2015}
}
备注
latex, 20 pages, references clarified, final version, to appear in J. Goem. Phys