Ruled minimal surfaces in the three-dimensional heisenberg group

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

doi:10.2140/pjm.2013.261.477

Ruled minimal surfaces in the three-dimensional heisenberg group

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

Department of Mathematics

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

8 Citations (Scopus)

Abstract

It is shown that parts of planes, helicoids and hyperbolic paraboloids are the only minimal surfaces ruled by geodesics in the three-dimensional Riemannian Heisenberg group. It is also shown that they are the only surfaces in the three-dimensional Heisenberg group whose mean curvature is zero with respect to both the standard Riemannian metric and the standard Lorentzian metric.

Original language	English
Pages (from-to)	477-496
Number of pages	20
Journal	Pacific Journal of Mathematics
Volume	261
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2013.261.477
Publication status	Published - 2013

Keywords

Heisenberg group
Minimal surface
Ruled surface

ASJC Scopus subject areas

Mathematics(all)

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10.2140/pjm.2013.261.477

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title = "Ruled minimal surfaces in the three-dimensional heisenberg group",

abstract = "It is shown that parts of planes, helicoids and hyperbolic paraboloids are the only minimal surfaces ruled by geodesics in the three-dimensional Riemannian Heisenberg group. It is also shown that they are the only surfaces in the three-dimensional Heisenberg group whose mean curvature is zero with respect to both the standard Riemannian metric and the standard Lorentzian metric.",

keywords = "Heisenberg group, Minimal surface, Ruled surface",

author = "Heayong Shin and Kim, {Young Wook} and Koh, {Sung Eun} and Lee, {Hyung Yong} and Yang, {Seong Deog}",

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T1 - Ruled minimal surfaces in the three-dimensional heisenberg group

AU - Shin, Heayong

AU - Kim, Young Wook

AU - Koh, Sung Eun

AU - Lee, Hyung Yong

AU - Yang, Seong Deog

PY - 2013

Y1 - 2013

N2 - It is shown that parts of planes, helicoids and hyperbolic paraboloids are the only minimal surfaces ruled by geodesics in the three-dimensional Riemannian Heisenberg group. It is also shown that they are the only surfaces in the three-dimensional Heisenberg group whose mean curvature is zero with respect to both the standard Riemannian metric and the standard Lorentzian metric.

AB - It is shown that parts of planes, helicoids and hyperbolic paraboloids are the only minimal surfaces ruled by geodesics in the three-dimensional Riemannian Heisenberg group. It is also shown that they are the only surfaces in the three-dimensional Heisenberg group whose mean curvature is zero with respect to both the standard Riemannian metric and the standard Lorentzian metric.

KW - Heisenberg group

KW - Minimal surface

KW - Ruled surface

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ER -

Ruled minimal surfaces in the three-dimensional heisenberg group

Abstract

Keywords

ASJC Scopus subject areas

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