*KCI등재*

*학술저널*

#
*ON CONSTRUCTIONS OF MINIMAL SURFACES*

- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 34, No. 1
- 등재여부 : KCI등재
- 2021.02
- 1 - 15 (15 pages)

In the recent papers, Sanchez-Reyes [Appl. Math. Model. 40 (2016), 1676{1682] described the method for nding a minimal surface through a geodesic, and Li et al. [Appl. Math. Model. 37 (2013), 6415{6424] studied the approximation of minimal surfaces with a geodesic from Dirichlet function. In the present article, we consider an isoparametric surface generated by Frenet frame of a curve introduced by Wang et al. [Comput. Aided Des. 36 (2004), 447-459], and give the necessary and sucient condition to satisfy both geodesic of the curve and minimality of the surface. From this, we construct minimal surfaces in terms of constant curvature and torsion of the curve. As a result, we present a new approach for constructions of the minimal surfaces from a prescribed closed geodesic and unclosed geodesic, and show some new examples of minimal surfaces with a circle and a helix as a geodesic. Our approach can be used in design of minimal surfaces from geodesics.

1. Introduction

2. Conditions of minimal surfaces

3. Constructions of minimal surfaces generated by curves

4. Representation of minimal surfaces with a geodesic

5. Conclusions