Algebraic constant mean curvature surfaces in Euclidean space

2010/02/01 by Oscar M. Perdomo, Perdomo, Oscar M.
Mathematics · #53A10 #53C42 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG #msc:53A10 #msc:53C42

paper · pdf · doi:10.48550/arxiv.1002.0174

7 pages

arxiv created 2010/02/01 · arxiv updated 2010/02/26

Abstract

In this paper we prove that the only algebraic constant mean curvature (cmc) surfaces in R³ of order less than four are the planes, the spheres and the cylinders. The method used heavily depends on the efficiency of algorithms to compute Groebner Bases and also on the memory capacity of the computer used to do the computations. We will also prove that the problem of finding algebraic constant mean curvature hypersurfaces in the Euclidean space completely reduces to the problem of solving a system of polynomial equations.

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