  If a compact quantum group acts isometrically on a (possibly discon- nected)
compact smooth Riemannian manifold such that the action commutes with the
Laplacian then it is known that the differential of the action preserves
Rieman- nian inner product on forms. In this note, we prove a partial converse
to this, under the additional assumption that the manifold is ori- ented and
the action preserves the orientation in a suitable sense. Using this an
alternative line of arguments is given for proving that there is no quantum
isometry for a compact, connected, Riemannian manifold.
