Surfaces whose Asymptotic Lines Constitute a Set of Parallels

In a recent paper by the present writer, it was shown that the Mainardi-Coddazi relations may be written :

^∂ _∂s(ψ²√-K) = + ψ²J K … (1)

and

^∂ _∂v(E √-K) = √E^∂ _∂u²(J ψ)v - (2)

constant being a system of asymptotic lines, k the curvature of the asymptotic line, and ψ the distance function for the family.