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 light-like 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 eachof the following conditions: (M,g) (resp., (M,widetilde g)) is locally symmetric, semisymmetric, Ricci semisymmetric 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.