Surfaces with constant Chebyshev angle (Q1943240)

A well-known fact is that one of the most common parameterizations of surfaces with negative Gaussian curvature is the Chebyshev net parameterization in Euclidean 3-space. The angle between the coordinate lines of this parameterization is called Chebyshev angle. The authors of this report characterize these surfaces in terms of a meromorphic function which satisfies a specific differential equation, which is analyzed in detail. An important application (corollary to the main result) associates a four-parameter family of complete surfaces to each constant Chebyshev angle.