An analogue of Bäcklund's theorem in affine geometry

The classical Bcklund theorem and its consequences. Let M be a surface in R 3 . We choose a local field of orthonormal frames v\, v<i, v$ with origin Xin R 3 such that X is a point of M and the vectors v\, v 2 are tangent to M at X. Let 0 1} 0 2 > 3 be the dual coframe of Vi, v 2 , #3. We can write