EQUIVALENCE OF CERTAIN SURFACES IN E3

The main task of this paper is to show that two isometric surfaces M: D → E^3and M bar : D → E^3 where D⊂R^2 is a bounded domain are equivalent provided that1- The Gauss curvature K of the surface M is positive K 0 2-The second fundamental forms II and II bar of the surfaces M and M bar respectively areequivalent on the bounding of D (∂D).