Ruled minimal surfaces in product spaces

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

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number6
Publication statusPublished - 2016

Bibliographical note

Funding Information:
Heayong Shin was supported by NRF 2014R1A2A2A01007324.

Publisher Copyright:
© 2016 Korean Mathematical Society.


  • Helicoid
  • Minimal surface
  • Ruled surface

ASJC Scopus subject areas

  • General Mathematics


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