Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures

Document Type: Research Paper

Author

Department of Algebra and Geometry‎, ‎Faculty of Mathematics and Informatics‎, ‎University of Veliko Tarnovo‎ ‎"St.‎ ‎Cyril and St‎. ‎Methodius"‎, ‎2 T. Tarnovski Str.‎, ‎5003 Veliko Tarnovo‎, ‎Bulgaria.

Abstract

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 $M$ by the Norden metrics $\overline g$ and $\overline {\widetilde g}$, respectively). We obtain a condition for $\overline {\widetilde \nu}$ (resp. $\overline \nu$) which is equivalent to each
of the following conditions: $(M,g)$ $(resp.\, (M,\widetilde g))$ is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein. We construct an example of a totally umbilical radical transversal lightlike hypersurface, which is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein.

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