Let
be an
-dimensional
hypersurface in
,
be the Laguerre
tensor,
be the Laguerre second fundamental form and
be the Laguerre form of the immersion
. The
purpose of this paper is to investigate Laguerre characterization
and rigidity of hypersurfaces in
. We firstly obtain
the classification of Laguerre isoparametric hypersurfaces with
three distinct Laguerre principal curvatures one of which is
simple and then we obtain a Laguerre rigidity result of
hypersurfaces in
.