Bulletin of the
Korean Mathematical Society BKMS

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1, f_2, f_3)$ admitting a generic lightlike submanifold $M$ subject such that the structure vector field of $\bar{M}(f_1, f_2, f_3)$ is tangent to $M$. The purpose of this paper is to prove a classification theorem of such an indefinite generalized Sasakian space form.

Keywords: indefinite generalized Sasakian space form, indefinite trans-Sasakian manifold, lightlike submanifold

MSC numbers: Primary 53C25, 53C40, 53C50