The construction of hyperbolic surfaces in 3 dimensional Minkowski space and sinh-Laplace equation. (English) Zbl 0594.53014
Der Zusammenhang zwischen Flächen konstanter negativer Krümmung im \(R^ 3\) und der sine-Gordon-Gleichung \(\alpha_{tt}-\alpha_{xx}=\pm \sin \alpha\) ist bekannt. Verf. studiert die Verallgemeinerung dieses Problems auf den Minkowski-Raum \(R^{2,1}\) und die sinh-Laplace- Gleichung
\[
\alpha_{tt}+\alpha_{xx}=\pm \sinh \alpha.
\]
Er demonstriert eine Methode für die Konstruktion von Flächen konstanter negativer Krümmung unter Anwendung von Tschebyschew-Koordinaten.
Reviewer: Z.Jankovský
Keywords:
sinh-Laplace equation; negative constant curvature; Minkowski; space; Chebyshev coordinatesReferences:
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