Volume 27, Issue 4, September 2020, Pages 529 - 549
Minimal surfaces associated with orthogonal polynomials
Authors
Vincent Chalifour
Departement of mathematics and statistics, Université de Montréal, C. P. 6128, Succ. Centre-ville, Montréal, Québec, H3C 3J7, Canada,chalifour@dms.umontreal.ca
Alfred Michel Grundland*
1Centre de Recherches Mathématiques, Université de Montréal, C. P. 6128, Succ. Centre-ville, Montréal, Québec, H3C 3J7, Canada
2Departement of Mathematics and Computer Science, Université du Québec, CP500, Trois-Rivières, Québec, G9A 5H7, Canada,grundlan@crm.umontreal.ca
*Corresponding author.
Corresponding Author
Alfred Michel Grundland
Received 17 January 2019, Accepted 3 December 2019, Available Online 4 September 2020.
- DOI
- 10.1080/14029251.2020.1819599How to use a DOI?
- Keywords
- Integrable system; soliton surface; minimal surface; orthogonal polynomial; Weierstrass immersion formula; Sym-Tafel immersion formula; CMC surface
- Abstract
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.
- Copyright
- © 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/).
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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 -