Generalized CR (GCR)-lightlike submanifolds of indefinite almost contact manifolds were
introduced by K. L. Duggal and B. Sahin, with the assumption that they are tangent to
the structure vector field ξ of the almost contact structure (φ,η,ξ ). Contrary to the above
assumption, we have introduced and studied a new class of CR-lightlike submanifold of
an indefinite nearly α-Sasakian manifold, called quasi generalized CR (QGCR)-lightlike
submanifold. We have showed that QGCR-lightlike submanifold include; ascreen QGCR,
co-screen QGCR and the well known GCR-lightlike submanifolds. We have proved some
existence (or non-existence) theorems and provided a thorough study of geometry of their
distributions. Also, we have constructed many examples, where necessary, to illustrate the
main ideas.
