Abstract
We provide definitions for the helicoidal Killing field and the helicoid in arbitrary three-manifolds, and investigate helicoids and ruled minimal surfaces in homogeneous three-manifolds, mainly in SL2ℝ and Sol(3). In so doing we finish our classification of ruled minimal surfaces in homogeneous three-manifolds with the isometry group of dimension 4.
| Original language | English |
|---|---|
| Pages (from-to) | 1235-1255 |
| Number of pages | 21 |
| Journal | Journal of the Korean Mathematical Society |
| Volume | 55 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2018 Jan 1 |
Keywords
- Helicoids
- Killing fields
- Ruled minimal surfaces
- Special linear group
ASJC Scopus subject areas
- Mathematics(all)
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Kim, Y. W., Koh, S. E., Lee, H. Y., Shin, H., & Yang, S-D. (2018). Helicoidal killing fields, helicoids and ruled minimal surfaces in homogeneous three-manifolds. Journal of the Korean Mathematical Society, 55(5), 1235-1255. https://doi.org/10.4134/JKMS.j170671