Algebraic constant mean curvature surfaces in Euclidean space

Autor:	Perdomo, Oscar M.
Rok vydání:	2010
Předmět:	Mathematics - Differential Geometry Mathematics - Algebraic Geometry 53C42 53A10
Druh dokumentu:	Working Paper
Popis:	In this paper we prove that the only algebraic constant mean curvature (cmc) surfaces in R^3 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. Comment: 7 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1002.0174 Zobrazit plný text záznamu View this record from Arxiv