  We show that statistical and semi-Weyl structures with torsion are invariant
under conformal-projective transformations. We prove that a non-degenerate
submanifold of a semi-Weyl (respectively, statistical) manifold with torsion is
also a semi-Weyl (respectively, statistical) manifold with torsion, and that
the induced structures of two conformal-projective equivalent semi-Weyl
(respectively, statistical) structures with torsion on a manifold to a
non-degenerate submanifold, are conformal-projective equivalent, too. Also, we
prove that the umbilical points of a non-degenerate hypersurface in a semi-Weyl
manifold with torsion are preserved by conformal-projective changes. Then we
consider lightlike hypersurfaces of semi-Weyl manifolds with torsion and we
describe similarities and differences with respect to the non-degenerate
hypersurfaces. Finally, we show that a semi-Weyl manifold with torsion can be
realized by a non-degenerate affine distribution.
