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BJORLING FORMULA FOR MEAN CURVATURE ONE SURFACES IN HYPERBOLIC THREE-SPACE AND IN DE SITTER THREE-SPACE
- Authors
- Yang, Seong-Deog
- Issue Date
- 1월-2017
- Publisher
- KOREAN MATHEMATICAL SOC
- Keywords
- Bjorling formula; constant mean curvature surfaces; de Sitter space
- Citation
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.54, no.1, pp.159 - 175
- Indexed
- SCIE
SCOPUS
KCI
- Journal Title
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
- Volume
- 54
- Number
- 1
- Start Page
- 159
- End Page
- 175
- ISSN
- 1015-8634
- Abstract
- We solve the Bjorling problem for constant mean curvature one surfaces in hyperbolic three-space and in de Sitter three-space. That is, we show that for any regular, analytic (and spacelike in the case of de Sitter three-space) curve gamma and an analytic (timelike in the case of de Sitter three-space) unit vector field N along and orthogonal to gamma, there exists a unique (spacelike in the case of de Sitter three-space) surface of constant mean curvature 1 which contains gamma and the unit normal of which on gamma is N. Some of the consequences are the planar reflection principles, and a classification of rotationally invariant CMC 1 surfaces.
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