2008/10/07 by Georgi Ganchev, Ganchev, Georgi
Mathematics · #53A07 #53A10 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.AP #math.DG #msc:53A07 #msc:53A10
paper · pdf · doi:10.48550/arxiv.0810.1235
14 pages
arxiv created 2008/10/07 · openalex publication_date 2008/10/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.