HELICOIDAL MINIMAL SURFACES in ℍ 2×ℝ

Young Wook Kim; Sung Eun Koh; Heayong Shin; Seong Deog Yang

doi:10.1017/S0004972711003042

HELICOIDAL MINIMAL SURFACES in ℍ ²×ℝ

Young Wook Kim, Sung Eun Koh, Heayong Shin, Seong Deog Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

It is shown that a minimal surface in ℍ ²× 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 ℍ ²× ℝ are certain types of catenoids.

Original language	English
Pages (from-to)	135-149
Number of pages	15
Journal	Bulletin of the Australian Mathematical Society
Volume	86
Issue number	1
DOIs	https://doi.org/10.1017/S0004972711003042
Publication status	Published - 2012 Aug

Keywords

associate minimal surfaces
catenoid
conjugate minimal surfaces
helicoid
helicoidal surface

ASJC Scopus subject areas

Mathematics(all)

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10.1017/S0004972711003042

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abstract = "It is shown that a minimal surface in ℍ 2× 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 ℍ 2× ℝ are certain types of catenoids.",

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AU - Yang, Seong Deog

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AB - It is shown that a minimal surface in ℍ 2× 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 ℍ 2× ℝ are certain types of catenoids.

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KW - catenoid

KW - conjugate minimal surfaces

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KW - helicoidal surface

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