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

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dc.creatorGanchev, Georgi
dc.date2008-10-07
dc.date.accessioned2026-07-07T10:08:09Z
dc.date.available2026-07-07T10:08:09Z
dc.descriptionWe 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.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0810.1235
dc.identifierhttp://arxiv.org/abs/0810.1235
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170894
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53A07; 53A10
dc.titleMinimal Surfaces in the Three-Dimensional Sphere and Minimal Hypersurfaces of Type Number Two
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