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HELICOIDAL MINIMAL SURFACES IN ℍ2×ℝ

Part of: Classical differential geometry

Published online by Cambridge University Press:  15 December 2011

YOUNG WOOK KIM ,
SUNG-EUN KOH ,
HEAYONG SHIN  and
SEONG-DEOG YANG
YOUNG WOOK KIM
Affiliation:
Dept. of Mathematics, Korea University, Seoul 136-701, Korea (email: ywkim@korea.ac.kr)
SUNG-EUN KOH*
Affiliation:
Dept. of Mathematics, Konkuk University, Seoul 143-701, Korea (email: skoh@konkuk.ac.kr)
HEAYONG SHIN
Affiliation:
Dept. of Mathematics, Chung-Ang University, Seoul 156-756, Korea (email: hshin@cau.ac.kr)
SEONG-DEOG YANG
Affiliation:
Dept. of Mathematics, Korea University, Seoul 136-701, Korea (email: sdyang@korea.ac.kr)
*
✉For correspondence; e-mail: skoh@konkuk.ac.kr
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Abstract

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It is shown that a minimal surface in ℍ2×ℝ is invariant under a one-parameter group of screw motions if and only if it lies in the associate family of helicoids. It is also shown that the conjugate surfaces of the parabolic and hyperbolic helicoids in ℍ2×ℝ are certain types of catenoids.

Keywords

helicoidal surfacehelicoidcatenoidassociate minimal surfacesconjugate minimal surfaces

MSC classification

Secondary: 53A35: Non-Euclidean differential geometry
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 1 , August 2012 , pp. 135 - 149
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The first named author was supported by NRF 2009-0086794. The second named author was supported by NRF 2009-0086794 and NRF 2009-0086441.

References

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