Communications of the
Korean Mathematical Society CKMS

We study two types of $1$-lightlike submanifolds, so-called lightlike hypersurface and half lightlike submanifold, of an indefinite trans-Sasakian manifold $\bar{M}$ admitting non-metric $\theta$-connection. We prove that there exist no such two types of $1$-lightlike submanifolds of an indefinite trans-Sasakian manifold $\bar{M}$ admitting non-metric $\theta$-connections.

Keywords: non-metric $\theta$-connections, lightlike hypersurface, half lightlike submanifold

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