The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space
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Publication:1822768
DOI10.2748/tmj/1178227694zbMath0679.53002OpenAlexW1998356197MaRDI QIDQ1822768
Seiki Nishikawa, Kazuo Akutagawa
Publication date: 1990
Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2748/tmj/1178227694
Gauss mapMinkowski 3-spacetension fieldprescribed mean curvtureWeierstrass Enneper-Kenmotsu representation formula
Global submanifolds (53C40) Surfaces in Euclidean and related spaces (53A05) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)
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Cites Work
- Unnamed Item
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- Maximal surfaces in the 3-dimensional Minkowski space \(L^ 3\)
- Maximal surfaces with conelike singularities
- Weierstrass formula for surfaces of prescribed mean curvature
- Harmonic Maps and Classical Surface Theory in Minkowski 3-Space
- A Report on Harmonic Maps
- The Tension Field of the Gauss Map