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

On in-plane drill rotations for Cosserat surfaces