Ruled minimal surfaces in the three-dimensional heisenberg group

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

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


It is shown that parts of planes, helicoids and hyperbolic paraboloids are the only minimal surfaces ruled by geodesics in the three-dimensional Riemannian Heisenberg group. It is also shown that they are the only surfaces in the three-dimensional Heisenberg group whose mean curvature is zero with respect to both the standard Riemannian metric and the standard Lorentzian metric.

Original languageEnglish
Pages (from-to)477-496
Number of pages20
JournalPacific Journal of Mathematics
Issue number2
Publication statusPublished - 2013


  • Heisenberg group
  • Minimal surface
  • Ruled surface

ASJC Scopus subject areas

  • Mathematics(all)


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