Helicoidal killing fields, helicoids and ruled minimal surfaces in homogeneous three-manifolds

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

doi:10.4134/JKMS.j170671

Helicoidal killing fields, helicoids and ruled minimal surfaces in homogeneous three-manifolds

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

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

Abstract

We provide definitions for the helicoidal Killing field and the helicoid in arbitrary three-manifolds, and investigate helicoids and ruled minimal surfaces in homogeneous three-manifolds, mainly in SL₂ℝ and Sol(3). In so doing we finish our classification of ruled minimal surfaces in homogeneous three-manifolds with the isometry group of dimension 4.

Original language	English
Pages (from-to)	1235-1255
Number of pages	21
Journal	Journal of the Korean Mathematical Society
Volume	55
Issue number	5
DOIs	https://doi.org/10.4134/JKMS.j170671
Publication status	Published - 2018

Bibliographical note

Funding Information:
Received October 20, 2017; Accepted April 9, 2018. 2010 Mathematics Subject Classification. 53A10, 53A35, 53C30. Key words and phrases. ruled minimal surfaces, special linear group, Killing fields, helicoids. Sung-Eun Koh was supported by NRF 2014R1A1A2002058 and NRF 2017060377, Heay-ong Shin was supported by NRF 2014R1A2A2A01007324 and Chung-Ang University research grant in 2017, Seong-Deog Yang was supported by NRF 2012-042530 and NRF 2017 R1E1A1A 03070929.

Funding Information:
Sung-Eun Koh was supported by NRF2014R1A1A2002058 and NRF2017060377, Heayong Shin was supported by NRF 2014R1A2A2A01007324 and Chung-Ang University research grant in 2017, Seong-Deog Yang was supported by NRF 2012-042530 and NRF 2017 R1E1A1A 03070929.

Keywords

Helicoids
Killing fields
Ruled minimal surfaces
Special linear group

ASJC Scopus subject areas

General Mathematics

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10.4134/JKMS.j170671

Cite this

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title = "Helicoidal killing fields, helicoids and ruled minimal surfaces in homogeneous three-manifolds",

abstract = "We provide definitions for the helicoidal Killing field and the helicoid in arbitrary three-manifolds, and investigate helicoids and ruled minimal surfaces in homogeneous three-manifolds, mainly in SL2ℝ and Sol(3). In so doing we finish our classification of ruled minimal surfaces in homogeneous three-manifolds with the isometry group of dimension 4.",

keywords = "Helicoids, Killing fields, Ruled minimal surfaces, Special linear group",

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

note = "Funding Information: Received October 20, 2017; Accepted April 9, 2018. 2010 Mathematics Subject Classification. 53A10, 53A35, 53C30. Key words and phrases. ruled minimal surfaces, special linear group, Killing fields, helicoids. Sung-Eun Koh was supported by NRF 2014R1A1A2002058 and NRF 2017060377, Heay-ong Shin was supported by NRF 2014R1A2A2A01007324 and Chung-Ang University research grant in 2017, Seong-Deog Yang was supported by NRF 2012-042530 and NRF 2017 R1E1A1A 03070929. Funding Information: Sung-Eun Koh was supported by NRF2014R1A1A2002058 and NRF2017060377, Heayong Shin was supported by NRF 2014R1A2A2A01007324 and Chung-Ang University research grant in 2017, Seong-Deog Yang was supported by NRF 2012-042530 and NRF 2017 R1E1A1A 03070929.",

year = "2018",

doi = "10.4134/JKMS.j170671",

language = "English",

volume = "55",

pages = "1235--1255",

journal = "Journal of the Korean Mathematical Society",

issn = "0304-9914",

publisher = "Korean Mathematical Society",

number = "5",

}

TY - JOUR

T1 - Helicoidal killing fields, helicoids and ruled minimal surfaces in homogeneous three-manifolds

AU - Kim, Young Wook

AU - Koh, Sung Eun

AU - Lee, Hyung Yong

AU - Shin, Heayong

AU - Yang, Seong Deog

N1 - Funding Information: Received October 20, 2017; Accepted April 9, 2018. 2010 Mathematics Subject Classification. 53A10, 53A35, 53C30. Key words and phrases. ruled minimal surfaces, special linear group, Killing fields, helicoids. Sung-Eun Koh was supported by NRF 2014R1A1A2002058 and NRF 2017060377, Heay-ong Shin was supported by NRF 2014R1A2A2A01007324 and Chung-Ang University research grant in 2017, Seong-Deog Yang was supported by NRF 2012-042530 and NRF 2017 R1E1A1A 03070929. Funding Information: Sung-Eun Koh was supported by NRF2014R1A1A2002058 and NRF2017060377, Heayong Shin was supported by NRF 2014R1A2A2A01007324 and Chung-Ang University research grant in 2017, Seong-Deog Yang was supported by NRF 2012-042530 and NRF 2017 R1E1A1A 03070929.

PY - 2018

Y1 - 2018

N2 - We provide definitions for the helicoidal Killing field and the helicoid in arbitrary three-manifolds, and investigate helicoids and ruled minimal surfaces in homogeneous three-manifolds, mainly in SL2ℝ and Sol(3). In so doing we finish our classification of ruled minimal surfaces in homogeneous three-manifolds with the isometry group of dimension 4.

AB - We provide definitions for the helicoidal Killing field and the helicoid in arbitrary three-manifolds, and investigate helicoids and ruled minimal surfaces in homogeneous three-manifolds, mainly in SL2ℝ and Sol(3). In so doing we finish our classification of ruled minimal surfaces in homogeneous three-manifolds with the isometry group of dimension 4.

KW - Helicoids

KW - Killing fields

KW - Ruled minimal surfaces

KW - Special linear group

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VL - 55

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JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 5

ER -

Helicoidal killing fields, helicoids and ruled minimal surfaces in homogeneous three-manifolds

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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