Surfaces at a constant distance from the edge of regression on a surface (Q1883154)

A parallel surface \(M_r\) to a given surface \(M\) is defined by adding the \(r\)-fold of the unit normal vectors \(N_P\) of \(M\) to the position vectors \(P\) of \(M\), where \(r\) is a given constant. The authors generalize this construction replacing the normal vectors \(N_P\) by unit vectors \(Z_P\) which have constant angle with the vectors \(N_P\). The surface \(M^f\) defined by \(P + r Z_P\) is then called surface at a constant distance from the edge of regression on \(M\) (the reviewer can not see any reason for this name and there is also no explanation in the paper). It is investigated how the shape operator \(S^f\), the Gauss curvature \(K^f\) and the mean curvature \(H^f\) of \(M^f\) depend on the corresponding values \(S\), \(K\) and \(H\) of \(M\).