Original scientific paper

On Algebraic Minimal Surfaces

Boris Odehnal orcid.org/0000-0002-7265-5132 ; University of Applied Arts Vienna, Vienna, Austria

Abstract

We give an overiew on various constructions of algebraic minimal surfaces in Euclidean three-space. Especially low degree examples shall be studied. For that purpose, we use the different representations given by WEIERSTRASS including the so-called Bjorling formula. An old result by LIE dealing with the evolutes of space curves can also be used to construct minimal surfaces with rational parametrizations. We describe a one-parameter family of
rational minimal surfaces which touch orthogonal hyperbolic paraboloids along their curves of constant Gaussian curvature. Furthermore, we find a new class of algebraic and even rationally parametrizable minimal surfaces and call them cycloidal minimal surfaces.

Keywords

minimal surface; algebraic surface; rational parametrization; polynomial parametrization; meromorphic function; isotropic curve; Weierstrass representation; Bjorling formula; evolute of a spacecurve; curve of constant slope

Hrčak ID:

174103

URI

https://hrcak.srce.hr/174103

Publication date:

16.1.2017.

Article data in other languages: croatian

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