On para-Norden metric connections

Distinguished Connections on (j2 = ±1)-metric Manifolds

We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of (J2 = ±1)-metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among con...

A Connection with Parallel Torsion on Almost Hypercomplex Manifolds with Norden Metric

Almost hypercomplex manifolds with Norden metric are considered. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the locally conformally equivalent manifolds to the hyper-Kähler manifolds with Norden metric and the case when the torsion of D is D-parallel. Curvature properties of these manifolds ar...

On three-parametric Lie groups as quasi-Kähler manifolds with Killing Norden metric

It is a fundamental fact that on an almost complex manifold with Hermitian metric (almost Hermitian manifold), the action of the almost complex structure on the tangent space at each point of the manifold is isometry. There is another kind of metric, called a Norden metric or a B-metric on an almost complex manifold, such that the action of the almost complex structure is anti-isometry with res...

On the Curvature Properties of Real Time-like Hypersurfaces of Kähler Manifolds with Norden Metric

A type of almost contact hypersurfaces with Norden metric of a Kähler manifold with Norden metric is considered. The curvature tensor and the special sectional curvatures are characterized. The canonical connection on such manifolds is studied and the form of the corresponding Kähler curvature tensor is obtained. Some curvature properties of the manifolds belonging to the widest integrable main...

Shen's Processes on Finslerian Connections