NON-EXISTENCE OF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE TRANS-SASAKIAN MANIFOLDS WITH NON-METRIC 𝜃-CONNECTIONS

Abstract

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