  We show under some natural smoothness assumptions that pure in-plane drill
rotations as deformation mappings of a $C^2$-smooth regular shell surface to
another one parametrized over the same domain are impossible provided that the
rotations are fixed at a portion of the boundary. Put otherwise, if the tangent
vectors of the new surface are obtained locally by only rotating the given
tangent vectors, and if these rotations have a rotation axis which coincides
everywhere with the normal of the initial surface, then the two surfaces are
equal provided they coincide at a portion of the boundary. In the language of
differential geometry of surfaces we show that any isometry which leaves
normals invariant and which coincides with the given surface at a portion of
the boundary, is the identity mapping.
