  We introduce canonical principal parameters on any strongly regular minimal
surface in the three dimensional sphere and prove that any such a surface is
determined up to a motion by its normal curvature function satisfying the
Sinh-Poisson equation. We obtain a classification theorem for bi-umbilical
hypersurfaces of type number two. We prove that any minimal hypersurface of
type number two with involutive distribution is generated by a minimal surface
in the three-dimensional Euclidean space, or in the three dimensional sphere.
Thus we prove that the theory of minimal hypersurfaces of type number two with
involutive distribution is locally equivalent to the theory of minimal surfaces
in the three dimensional Euclidean space or in the three-dimensional sphere.
