On weyl's identity in the differential geometry of surfaces

Summary At the end of his classical paper on convex surfaces in thelarge,H. Weyl (1916) gave an identity connecting the first and second fundamental forms of a surface. The identity is, however, a purelylocal relation and it holds also when the Gaussian curvature, instead of being positive, is negative. The present paper centers around this identity. Various applications of it are considered and the conditions of validity are specified.