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

Department of Mathematics

Research output: Contribution to journal › Article

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 Jan 1

Fingerprint

Keywords

Helicoids
Killing fields
Ruled minimal surfaces
Special linear group

ASJC Scopus subject areas

Mathematics(all)

Cite this

Kim, Y. W., Koh, S. E., Lee, H. Y., Shin, H., & Yang, S-D. (2018). Helicoidal killing fields, helicoids and ruled minimal surfaces in homogeneous three-manifolds. Journal of the Korean Mathematical Society, 55(5), 1235-1255. https://doi.org/10.4134/JKMS.j170671

@article{c3e3c0b8ba724e4fac428c215a8d4b71,

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 Seong-Deog Yang",

year = "2018",

month = "1",

day = "1",

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

PY - 2018/1/1

Y1 - 2018/1/1

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

UR - http://www.scopus.com/inward/record.url?scp=85052739819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052739819&partnerID=8YFLogxK

U2 - 10.4134/JKMS.j170671

DO - 10.4134/JKMS.j170671

M3 - Article

AN - SCOPUS:85052739819

VL - 55

SP - 1235

EP - 1255

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

SN - 0304-9914

IS - 5

ER -

Access to Document

10.4134/JKMS.j170671