Helicoids in 𝕊2 × ℝ and ℍ2 × ℝ

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

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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 languageEnglish
Pages (from-to)281-297
Number of pages17
JournalPacific Journal of Mathematics
Issue number2
Publication statusPublished - 2009 Oct


  • Helicoid
  • Minimal surface
  • Ruled surface
  • Spacelike maximal surface

ASJC Scopus subject areas

  • General Mathematics


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