η\eta-Ricci solitons in (ε)(\varepsilon)-almost paracontact metric manifolds

The object of this paper is to study $\eta$-Ricci solitons on $(\varepsilon)$-almost paracontact metric manifolds. We investigate $\eta$-Ricci solitons in the case when its potential vector field is exactly the characteristic vector field $\xi$ of the $(\varepsilon)$-almost paracontact metric manifold and when the potential vector field is torse-forming. We also study Einstein-like and $(\varepsilon)$-para Sasakian manifolds admitting $\eta$-Ricci solitons. Finally we obtain some results for $\eta$-Ricci solitons on $(\varepsilon)$-almost paracontact metric manifolds with a special view towards parallel symmetric (0,2)-tensor fields.Comment: 20 page

On Lightlike Geometry of Para-Sasakian Manifolds

We study lightlike hypersurfaces of para-Sasakian manifolds tangent to the characteristic vector field. In particular, we define invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, respectively, and give examples. Integrability conditions for the distributions on a screen semi-invariant lightlike hypersurface of para-Sasakian manifolds are investigated. We obtain a para-Sasakian structure on the leaves of an integrable distribution of a screen semi-invariant lightlike hypersurface

SCREEN SLANT RADICAL TRANSVERSAL NULL SUBMANIFOLDS OF PARA-SASAKIAN MANIFOLDS

In our paper we introduce totally paracontact umbilical radical transversalnull submanifolds and screen slant radical transversal null submanifolds of para-Sasakian manifolds. On a screen slant radical transversal null submanifold of a para-Sasakian manifold, we find integrability conditions of distributions