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We show how the rotation and translation fields of a surface, introduced byG. Darboux, may be used to obtain short proofs of a well-known theorem (thatreads that the total mean curvature of a surface is stationary under aninfinitesimal bending) and a new theorem (that reads that every infinitesimalflex of any simply connected closed surface is orthogonal to the surface atleast at two points).

New manifestations of the Darboux's rotation and translation fields of a surface