Global differential geometry of surfaces in affine space

For a surface in the affine space A 3 a certain tensor is defined, this tensor being the fundamental object for surfaces with non-planar points.S. SASAKI has proved the following theorem (see [1], Theorem 4, p. 81): In the Euclidean space E 3 , let two surfaces S, S' and a diffeomorphism C : S -» S' be given.If the first and second tensors are equal at the points pe S and C(p) e S' for each peS, then the surfaces S and S' are globally equal, i. e. there exists an isometry 5 : E 3 -+ E 3 such that 3(p) == C(p) for each pe S. In this paper, I define a certain tensor field on a surface of the affine space A 3 , and prove a theorem which is analoguous to that of Sasaki.