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Self θ-congruent minimal surfaces in ℝ3

Part of: Classical differential geometry

Published online by Cambridge University Press:  09 April 2009

Weihuan Chen  and
Yi Fang
Weihuan Chen
Affiliation:
School of Mathematical Sciences Peking UniversityBeijing 100871China e-mail: [email protected]
Yi Fang
Affiliation:
Center for Mathematics and its Applications School of Mathematical Sciences Australian National UniversityCanberra, ACT 0200Australia e-mail: [email protected]
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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.

Keywords

minimal surfaceself-congruenceEuclidean 3-space

MSC classification

Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 2 , October 2000 , pp. 229 - 244
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), 359–371.Google Scholar
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[3]Kobayashi, O., ‘Maximal surfaces in the 3-dimensional Minkowski space L3’, Tokyo J. Math. 6 (1983), 297–309.CrossRefGoogle Scholar
[4]Osserman, R., A survey of minimal surfaces (Dover, New York, 1986).Google Scholar