Communications of the
Korean Mathematical Society CKMS

The notion of a {\it non-metric $\phi$-symmetric connection} on semi-Riemannian manifolds was introduced by Jin \cite{Jin4, Jin5}. The object of study in this paper is generic lightlike submanifolds of an indefinite Kaehler manifold $\bar{M}$ with a non-metric $\phi$-symmetric connection. First, we provide several new results for such generic lightlike submanifolds. Next, we investigate generic lightlike submanifolds of an indefinite complex space form $\bar{M}(c)$ with a non-metric $\phi$-symmetric connection.

Keywords: non-metric $\phi$-symmetric connection, generic lightlike submanifold, indefinite Kaehler structure

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