Helicoids in 𝕊2 × ℝ and ℍ2 × ℝ

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

doi:10.2140/pjm.2009.242.281

Helicoids in 𝕊2 × ℝ and ℍ2 × ℝ

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

Department of Mathematics

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

9 Citations (Scopus)

Abstract

We provide two characterizations of helicoids in S{double-struck}² × R{double-struck} and in H² × R. First, we show that any nontrivial ruled minimal surface in S{double-struck}² × R{double-struck} and in H{double-struck}² × R{double-struck} is a part of a helicoid. Second, we also show that these surfaces can be characterized as the only surface with zero mean curvature with respect to both the Riemannian product metric and the Lorentzian product metric on S{double-struck}² × R{double-struck} or H{double-struck}² × R{double-struck}.

Original language	English
Pages (from-to)	281-297
Number of pages	17
Journal	Pacific Journal of Mathematics
Volume	242
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2009.242.281
Publication status	Published - 2009 Oct

Keywords

Helicoid
Minimal surface
Ruled surface
Spacelike maximal surface

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.2140/pjm.2009.242.281

Fingerprint Dive into the research topics of 'Helicoids in 𝕊2 × ℝ and ℍ2 × ℝ'. Together they form a unique fingerprint.

Cite this

@article{c664747984e24a75a6ac5e5102e9ff2c,

title = "Helicoids in 핊2 × ℝ and ℍ2 × ℝ",

abstract = "We provide two characterizations of helicoids in S{double-struck}2 × R{double-struck} and in H2 × R. First, we show that any nontrivial ruled minimal surface in S{double-struck}2 × R{double-struck} and in H{double-struck}2 × R{double-struck} is a part of a helicoid. Second, we also show that these surfaces can be characterized as the only surface with zero mean curvature with respect to both the Riemannian product metric and the Lorentzian product metric on S{double-struck}2 × R{double-struck} or H{double-struck}2 × R{double-struck}.",

keywords = "Helicoid, Minimal surface, Ruled surface, Spacelike maximal surface",

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

year = "2009",

month = oct,

doi = "10.2140/pjm.2009.242.281",

language = "English",

volume = "242",

pages = "281--297",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "University of California, Berkeley",

number = "2",

}

TY - JOUR

T1 - Helicoids in 핊2 × ℝ and ℍ2 × ℝ

AU - Kim, Young Wook

AU - Koh, Sung Eun

AU - Shin, Heayong

AU - Yang, Seong Deog

PY - 2009/10

Y1 - 2009/10

N2 - We provide two characterizations of helicoids in S{double-struck}2 × R{double-struck} and in H2 × R. First, we show that any nontrivial ruled minimal surface in S{double-struck}2 × R{double-struck} and in H{double-struck}2 × R{double-struck} is a part of a helicoid. Second, we also show that these surfaces can be characterized as the only surface with zero mean curvature with respect to both the Riemannian product metric and the Lorentzian product metric on S{double-struck}2 × R{double-struck} or H{double-struck}2 × R{double-struck}.

AB - We provide two characterizations of helicoids in S{double-struck}2 × R{double-struck} and in H2 × R. First, we show that any nontrivial ruled minimal surface in S{double-struck}2 × R{double-struck} and in H{double-struck}2 × R{double-struck} is a part of a helicoid. Second, we also show that these surfaces can be characterized as the only surface with zero mean curvature with respect to both the Riemannian product metric and the Lorentzian product metric on S{double-struck}2 × R{double-struck} or H{double-struck}2 × R{double-struck}.

KW - Helicoid

KW - Minimal surface

KW - Ruled surface

KW - Spacelike maximal surface

UR - http://www.scopus.com/inward/record.url?scp=70349774270&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349774270&partnerID=8YFLogxK

U2 - 10.2140/pjm.2009.242.281

DO - 10.2140/pjm.2009.242.281

M3 - Article

AN - SCOPUS:70349774270

VL - 242

SP - 281

EP - 297

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -

Helicoids in 𝕊2 × ℝ and ℍ2 × ℝ

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this