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 journalArticle

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 languageEnglish
Pages (from-to)1235-1255
Number of pages21
JournalJournal of the Korean Mathematical Society
Volume55
Issue number5
DOIs
Publication statusPublished - 2018 Jan 1

Keywords

  • Helicoids
  • Killing fields
  • Ruled minimal surfaces
  • Special linear group

ASJC Scopus subject areas

  • Mathematics(all)

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