@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 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",
}