%0 Journal Article
%T A connection with parallel totally skew-symmetric torsion on a class of almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics
%A Mancho Manev
%A Kostadin Gribachev
%J Mathematics
%D 2010
%I arXiv
%R 10.1142/S0219887811005026
%X The subject of investigations are the almost hypercomplex manifolds with Hermitian and anti-Hermitian (Norden) metrics. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D and its torsion is totally skew-symmetric. The class of the nearly Kaehler manifolds with respect to the first almost complex structure is of special interest. It is proved that D has a D-parallel torsion and is weak if it is not flat. Some curvature properties of these manifolds are studied.
%U http://arxiv.org/abs/1003.2051v1