Helicoids in S{double-struck}2 × R{double-struck} and H{double-struck}2 × R{double-struck}

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

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume242
Issue number2
DOIs
Publication statusPublished - 2009 Oct 1

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Helicoid
Metric
Ruled Surface
Minimal surface
Mean Curvature
Zero

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Helicoids in S{double-struck}2 × R{double-struck} and H{double-struck}2 × R{double-struck}. / Kim, Young Wook; Koh, Sung Eun; Shin, Heayong; Yang, Seong-Deog.

In: Pacific Journal of Mathematics, Vol. 242, No. 2, 01.10.2009, p. 281-297.

Research output: Contribution to journalArticle

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