On the Curvature Properties of Real Time-like Hypersurfaces of Kähler Manifolds with Norden Metric
نویسنده
چکیده
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 class of the considered type of hypersurfaces are given.∗
منابع مشابه
Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures
In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...
متن کاملContact Hypersurfaces in Kähler Manifolds
A contact hypersurface in a Kähler manifold is a real hypersurface for which the induced almost contact metric structure determines a contact structure. We carry out a systematic study of contact hypersurfaces in Kähler manifolds. We then apply these general results to obtain classifications of contact hypersurfaces with constant mean curvature in the complex quadric Q = SOn+2/SOnSO2 and its no...
متن کاملA 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...
متن کاملKähler Metrics Generated by Functions of the Time-like Distance in the Flat Kähler-lorentz Space
We prove that every Kähler metric, whose potential is a function of the timelike distance in the flat Kähler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kähler manifolds with the above mentioned metrics. New examples of Sasakian space forms are obtained as real hypersurfaces of a Kähler space form ...
متن کاملOn 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...
متن کامل