Bäcklund transformations for surfaces in Minkowski space. (English) Zbl 0722.53058
Summary: A Bäcklund transformation is constructed between spacelike surfaces of constant negative curvature and timelike surfaces of constant negative curvature in three-dimensional Minkowski space. The transformation gives a differential geometric interpretation to a Bäcklund transformation between the elliptic sine-Gordon equation and the elliptic sinh-Gordon equation studied by G. Leibbrandt [ibid. 19, 960-966 (1978; Zbl 0383.35021)].
MSC:
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
| 53C40 | Global submanifolds |
Keywords:
Bäcklund transformation; spacelike surfaces; constant negative curvature; timelike surfaces; Minkowski spaceCitations:
Zbl 0383.35021References:
| [1] | DOI: 10.1063/1.523799 · Zbl 0383.35021 · doi:10.1063/1.523799 |
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