Rigidifying curves on surfaces

The infinitesimal rigidity of surfaces is addressed in this Note. Let us co nsider a bidimensional metric manifold imbedded in R-3: we seek the infinit esimal changes of imbedding conserving its metric to first order A criterio n for the existence of such deformations is presented in the particular cas e of surfaces of revolution. It reveals rigidifying curves on the surface, called "a-curves". A geometric interpretation of the rigidity brought about by a-curves leads to the identification of rigidifying curves on arbitrary surfaces. (C) Academie des Sciences/Elsevier, Paris.