Minimal surfaces associated with orthogonal polynomials
- 10.1080/14029251.2020.1819599How to use a DOI?
- Integrable system; soliton surface; minimal surface; orthogonal polynomial; Weierstrass immersion formula; Sym-Tafel immersion formula; CMC surface
This paper is devoted to a study of the connection between the immersion functions of two-dimensional surfaces in Euclidean or hyperbolic spaces and classical orthogonal polynomials. After a brief description of the soliton surfaces approach defined by the Enneper-Weierstrass formula for immersion and the solutions of the Gauss-Weingarten equations for moving frames, we derive the three-dimensional numerical representation for these polynomials. We illustrate the theoretical results for several examples, including the Bessel, Legendre, Laguerre, Chebyshev and Jacobi functions. In each case, we generate a numerical representation of the surface using the Mathematica symbolic software.
- © 2020 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Vincent Chalifour AU - Alfred Michel Grundland PY - 2020 DA - 2020/09/04 TI - Minimal surfaces associated with orthogonal polynomials JO - Journal of Nonlinear Mathematical Physics SP - 529 EP - 549 VL - 27 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2020.1819599 DO - 10.1080/14029251.2020.1819599 ID - Chalifour2020 ER -