Abstract : We study the geometry of indefinite trans-Sasakian manifold $\bar{M}$, of type $(\alpha, \beta)$, admitting a half lightlike submanifold $M$ such that the structure vector field of $\bar{M}$ does not belong to the screen and coscreen distributions of $M$. The purpose of this paper is to prove several classification theorems of such an indefinite trans-Sasakian manifold.
