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 journalArticle

5 Citations (Scopus)

Abstract

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
Volume261
Issue number2
DOIs
Publication statusPublished - 2013 Jun 12

Fingerprint

Ruled Surface
Heisenberg Group
Minimal surface
Three-dimensional
Riemannian Metric
Mean Curvature
Geodesic
Metric
Zero
Standards

Keywords

  • Heisenberg group
  • Minimal surface
  • Ruled surface

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Ruled minimal surfaces in the three-dimensional heisenberg group. / Shin, Heayong; Kim, Young Wook; Koh, Sung Eun; Lee, Hyung Yong; Yang, Seong-Deog.

In: Pacific Journal of Mathematics, Vol. 261, No. 2, 12.06.2013, p. 477-496.

Research output: Contribution to journalArticle

Shin, Heayong ; Kim, Young Wook ; Koh, Sung Eun ; Lee, Hyung Yong ; Yang, Seong-Deog. / Ruled minimal surfaces in the three-dimensional heisenberg group. In: Pacific Journal of Mathematics. 2013 ; Vol. 261, No. 2. pp. 477-496.
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