On the conformal mapping of orthogonal surfaces in \(E^{2n}\). (Q1810028)

Let \(M\) and \(\overline M\) be two smooth \(n\)-surfaces in the Euclidean space \(E^{2n}\) and \(f: M\to M\) be a diffeomorphism. The author gives the following two properties of the pair \((M,\overline M)\) related to \(f\) if \(f\) is a conformal mapping and, moreover, \(M\), \(\overline M\) are orthogonal related to \(f\), that is the case in which the tangents of the \(n\)-plane at the corresponding points \(p\in M\) and \(f(p)\in\overline M\) are orthogonal in \(E^{2n}\): 1. The Ricci tensors of the surfaces at the corresponding points coincide; 2. For two nonminimal such surfaces, \(f\) preserves the lines of curvature with respect to the mean normal vector.