A new class of semi-Riemannian and lightlike manifolds (including globally null) is
constructed by using a hypersurface of an orientable Riemannian manifold, endowed
with the second fundamental form instead of a metric induced from the ambient
space. We show the existence (or non-existence) of harmonic tensor fields and
harmonic maps and extend to the semi-Riemannian and lightlike case a result of
Chen-Nagano [4]. Then we deal with general lightlike submanifolds immersed in a
semi-Riemannian manifold and propose a definition of minimal lightlike
submanifolds, which generalize the one given in [7] in the Minkowski space
${\bf R}^4_1$ . Several examples are given throughout.