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 language | English |
|---|---|
| Pages (from-to) | 281-297 |
| Number of pages | 17 |
| Journal | Pacific Journal of Mathematics |
| Volume | 242 |
| Issue number | 2 |
| Publication status | Published - 2009 Oct |
Keywords
- Helicoid
- Minimal surface
- Ruled surface
- Spacelike maximal surface
ASJC Scopus subject areas
- Mathematics(all)
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Kim, Y. W., Koh, S. E., Shin, H., & Yang, S. D. (2009). Helicoids in 핊2 × ℝ and ℍ2 × ℝ. Pacific Journal of Mathematics, 242(2), 281-297.