  The common intrinsic geometry shared by all the null hypersurfaces gives rise
to the asymptotic symmetries found on the null infinities $\mathscr I^\pm$ and
the isolated horizons $\Delta$. In this work, the properties of a null
hypersurface are reviewed and the invariance of its intrinsic geometry
($n^an^bh_{ab}$) is revealed under the spacetime conformal transformation. The
generators, i.e., infinitesimal symmetries, of the conformal transformation
tangent to the null hypersurface are defined and classified by their effects on
the induced metric and the normal vector field. Two particular examples and
their symmetries are discussed, that is, the null infinities $\mathscr I^\pm$
of an asymptotic flat spacetime, and the isolated horizon $\Delta$ of a black
hole.
