Ruled minimal surfaces in product spaces

Yuzi Jin, Young Wook Kim, Namkyoung Park, Heayong Shin

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

It is well known that the helicoids are the only ruled minimal surfaces in ℝ3. The similar characterization for ruled minimal surfaces can be given in many other 3-dimensional homogeneous spaces. In this note we consider the product space M × ℝ for a 2-dimensional manifold M and prove that M ×ℝ has a nontrivial minimal surface ruled by horizontal geodesics only when M has a Clairaut parametrization. Moreover such minimal surface is the trace of the longitude rotating in M while translating vertically in constant speed in the direction of ℝ.

Original languageEnglish
Pages (from-to)1887-1892
Number of pages6
JournalBulletin of the Korean Mathematical Society
Volume53
Issue number6
DOIs
Publication statusPublished - 2016

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Keywords

  • Helicoid
  • Minimal surface
  • Ruled surface

ASJC Scopus subject areas

  • Mathematics(all)

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