Generalized euler formula for curvature

This study aims to show how to obtain the curvature of the ellipsoid for generalized surfaces. The curvature topic is quite popular at an interdisciplinary level. It can be to the friends of geometry, geodesy, satellite orbits in space, in studying all sorts of elliptical motions (e.g., planetary motions), curvature of surfaces and concerning eye-related radio-therapy treatment, for example the anterior surface of the cornea is often represented as ellipsoidal in form. On the calculation of the curvature, there is a famous Euler formula for rotating ellipsoid that everyone knows. I wonder how can a formula for the general surfaces (e.g. hyperboloid, triaxial ellipsoid)? so we started to work. In a way I generalize the Euler formula, and I gave the original a formula for it.