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Self θ-congruent minimal surfaces in ℝ3

Published online by Cambridge University Press:  09 April 2009

Weihuan Chen
Affiliation:
School of Mathematical Sciences Peking UniversityBeijing 100871China e-mail: whchen@pku.edu.cn
Yi Fang
Affiliation:
Center for Mathematics and its Applications School of Mathematical Sciences Australian National UniversityCanberra, ACT 0200Australia e-mail: yi@maths.anu.edu.au
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Abstract

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A minimal surface is a surface with vanishing mean curvature. In this paper we study self θ -congruent minimal surfaces, that is, surfaces which are congruent to their θ-associates under rigid motions in R3 for 0 ≤ θ < 2π. We give necessary and sufficient conditions in terms of its Weierstrass pair for a surface to be self θ-congruent. We also construct some examples and give an application.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Chen, W. H., ‘Characterization of self-conjugate minimal surfaces in R3’, Chinese J. Contemp. Math. 16 (1995), 359371.Google Scholar
[2]Fang, yi., Lectures on minimal surfaces in R3, in: Proceedings of CMA, vol. 35, Australian National University, Canberra (1996).Google Scholar
[3]Kobayashi, O., ‘Maximal surfaces in the 3-dimensional Minkowski space L3’, Tokyo J. Math. 6 (1983), 297309.CrossRefGoogle Scholar
[4]Osserman, R., A survey of minimal surfaces (Dover, New York, 1986).Google Scholar
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