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RULED MINIMAL SURFACES IN PRODUCT SPACES
- Authors
- Jin, Yuzi; Kim, Young Wook; Park, Namkyoung; Shin, Heayong
- Issue Date
- 11월-2016
- Publisher
- KOREAN MATHEMATICAL SOC
- Keywords
- ruled surface; minimal surface; helicoid
- Citation
- Bulletin of the Korean Mathematical Society, v.53, no.6, pp.1887 - 1892
- Indexed
- SCIE
SCOPUS
KCI
- Journal Title
- Bulletin of the Korean Mathematical Society
- Volume
- 53
- Number
- 6
- Start Page
- 1887
- End Page
- 1892
- ISSN
- 1015-8634
- Abstract
- It is well known that the helicoids are the only ruled minimal surfaces in R-3. 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 x R for a 2-dimensional manifold M and prove that M x 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.
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