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arXiv · 1912.10899

Minimal surfaces associated with orthogonal polynomials

Vincent Chalifour·Alfred Michel Grundland
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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.

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Vincent Chalifour, Alfred Michel Grundland. 2019-12-23. Minimal surfaces associated with orthogonal polynomials. https://arxiv.org/abs/1912.10899

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