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

^*Corresponding author for this work

Department of Mathematics

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

11 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

General Mathematics

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10.2140/pjm.2013.261.477

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@article{864f61201a764abf901442a9e6a52afc,

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\}",

year = "2013",

doi = "10.2140/pjm.2013.261.477",

language = "English",

volume = "261",

pages = "477--496",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "Mathematical Sciences Publishers",

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TY - JOUR

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

UR - https://www.scopus.com/pages/publications/84878736762

U2 - 10.2140/pjm.2013.261.477

DO - 10.2140/pjm.2013.261.477

M3 - Article

AN - SCOPUS:84878736762

SN - 0030-8730

VL - 261

SP - 477

EP - 496

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

Ruled minimal surfaces in the three-dimensional heisenberg group

Abstract

Keywords

ASJC Scopus subject areas

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