On pairs of hypersurfaces in Euclidean space (Q1889628)

\textit{K. Nomizu} and \textit{K. Yano} proved in [Math. Z. 97, 29--37 (1967; Zbl 0148.15602)] that a strongly curvature preserving diffeomorphism between irreducible analytic Riemannian manifolds of dimension \(\geq 2\) is a homothetic transformation. The author of the present paper proves that if \(f: M\to\overline M\) is a diffeomorphism of a pair of nondegenerate hypersurfaces in Euclidean space \(E^n\), \(n > 3\), preserving curvature tensors, then the first fundamental forms \(b\), \(\overline b\) of the hypersurfaces \(M\), \(\overline M\) satisfy the equations \(\overline g = t^2 g\), \(\overline b= tb\), \(t\in R\), \(\overline M\) can be locally obtained from \(M\) by means of a homothetic transformation and an isometry in \(E^n\).