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

Minimal Surfaces in the Three-Dimensional Sphere and Minimal Hypersurfaces of Type Number Two