Let be an almost Hermitian manifold. A submanifold of is called slant if for each and the angle between and is constant [B.-Y. Chen, Bull. Aust. Math. Soc. 41, No. 1, 135–147 (1990; Zbl 0677.53060)]. Special cases of slant submanifolds are almost complex () and totally real () submanifolds.
Let be a submanifold immersed in a semi-Riemannian manifold . The distribution is called the radical and its complementary distribution is called the screen distribution. A submanifold is called a light-like submanifold if is of rank [K. L. Duggal and A. Bejancu Lightlike submanifolds of semi-Riemannian manifolds and applications (Mathematics and its Applications Dordrecht: Kluwer Academic Publishers) (1996; Zbl 0848.53001)].
The goal of this paper is to introduce the notion of a slant light-like submanifold of an indefinite Hermitian manifold . The author proves a characterization theorem for the existence of slant light-like submanifolds and shows that co-isotropic -light-like submanifolds are slant light-like submanifolds. Also, minimal slant light-like submanifolds are presented and some examples and two characterization theorems are given.