5 research outputs found
On Lie groups as quasi-K\"ahler manifolds with Killing Norden metric
A 6-parametric family of 6--dimensional quasi-K\"ahler manifolds with Norden
metric is constructed on a Lie group. This family is characterized
geometrically.Comment: 11 pages, 2 table
A connection with parallel totally skew-symmetric torsion on a class of almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics
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.Comment: 18 page