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

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

2008-10-07

arxiv.org/abs/0810.1235v1

Mathematics

Differential Geometry

14 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Minimal Surfaces in the Three-Dimensional Sphere and Minimal Hypersurfaces of Type Number Two does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Minimal Surfaces in the Three-Dimensional Sphere and Minimal Hypersurfaces of Type Number Two, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimal Surfaces in the Three-Dimensional Sphere and Minimal Hypersurfaces of Type Number Two will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-557960