Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms

Abstract

We study lightlike hypersurfaces $M$ of an indefinite generalized Sasakian space form $\stackrel{-}{M}(f_1,f_2,f_3)$, with indefinite trans-Sasakian structure of type $(\alpha ,\beta )$, subject to the condition that the structure vector field of $\stackrel{-}{M}$ is tangent to $M$. First we study the general theory for lightlike hypersurfaces of indefinite trans-Sasakian manifold of type $(\alpha ,\beta )$. Next we prove several characterization theorems for lightlike hypersurfaces of an indefinite generalized Sasakian space form.