What is the differential equation of lines on the "oblique Chebychev Net" formed by connecting boundary points on a base circle to an apex point not on circle axis? ( base circle center to apex oblique connecting line is inclined at $\alpha \ne \pi/2) $ to the plane of circle.

Is negative Gauss curvature $K$ constant for this distorted surface? How is the Sine-Gordon equation modified?

Do lines seen in the idealized model still have zero normal curvature when internode distance tends to zero in the limit?

If $K$ is not constant, then how should the bottom circle be redefined as a new distorted oval for same constant $K$?



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