Slant and Hemislant Submanifolds of a 3-Dimensional Indefinite Trans-Sasakian Manifold

In this paper we would like to establish some of the properties of slant and hemislant sub- manifolds of an indefinite trans-Sasakian manifold. We have four sections in this paper. Section (1) is introductory. In Section (2) we recall some necessary details of an indefinite trans-Sasakian manifold. In Section (3) we have obtained some interesting properties on a totally umbilical slant submanifolds of an indefinite trans-Sasakian manifold. Finally, in Section (4), some results on integrability con- ditions of the distributions of hemislant submanifolds of an indefinite trans-Sasakian manifold have been obtained.