$2$--CODIMENSIONAL LIGHTLIKE SUBMANIFOLDS
OF ALMOST PARA--HERMITIAN MANIFOLDS

Cornelia--Livia BEJAN

1991 Math. Subject Classification: 53C40; 53C50; 53C15.

Key words: Degenerate submanifolds; para-Hermitian manifolds.

Introduction. Let $(\bar M,\bar g)$ be a semi--Riemannian
(pseudo--Riemannian) manifold, [10] and let $M$ be
a submanifold of it. If the restriction $g=\bar g/M$ of
$\bar g$ to $M$ is still non--degenerate, then \mg\ becomes
a semi--Riemannian manifold and it can be studied
as the submanifolds of Riemannian manifolds. A
different situation appears when $g$ is degenerate and \mg\
is said to be a lightlike (degenerate) submanifold,
[5], [6].

Among all semi--Riemannian manifolds, the class of the almost
para--Hermitian manifolds is of special interest and it was
considered by several authors, as in the list of references
of [4].

Bejancu and Etayo initiated in [7] the study of degenerate
hypersurfaces of almost para--Hermitian manifolds. Our purpose
here is to step from the hypersurfaces to the submanifolds of
arbitrary codimension. The present note deals with
degenerate submanifolds of codimension two of almost
para--Hermitian manifolds, since for higher codimension the
results are similar but the calculus is much longer. We
classify them, we prove their main properties and we also
give some examples.