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 |
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Pages (from-to) | 135-149 |
Number of pages | 15 |
Journal | Bulletin of the Australian Mathematical Society |
Volume | 86 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2012 Aug 1 |
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Keywords
- associate minimal surfaces
- catenoid
- conjugate minimal surfaces
- helicoid
- helicoidal surface
ASJC Scopus subject areas
- Mathematics(all)
Cite this
HELICOIDAL MINIMAL SURFACES in ℍ 2×ℝ. / Kim, Young Wook; Koh, Sung Eun; Shin, Heayong; Yang, Seong-Deog.
In: Bulletin of the Australian Mathematical Society, Vol. 86, No. 1, 01.08.2012, p. 135-149.Research output: Contribution to journal › Article
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TY - JOUR
T1 - HELICOIDAL MINIMAL SURFACES in ℍ 2×ℝ
AU - Kim, Young Wook
AU - Koh, Sung Eun
AU - Shin, Heayong
AU - Yang, Seong-Deog
PY - 2012/8/1
Y1 - 2012/8/1
N2 - 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.
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.
KW - associate minimal surfaces
KW - catenoid
KW - conjugate minimal surfaces
KW - helicoid
KW - helicoidal surface
UR - http://www.scopus.com/inward/record.url?scp=84864881351&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84864881351&partnerID=8YFLogxK
U2 - 10.1017/S0004972711003042
DO - 10.1017/S0004972711003042
M3 - Article
AN - SCOPUS:84864881351
VL - 86
SP - 135
EP - 149
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
SN - 0004-9727
IS - 1
ER -