Abstract
A Bäcklund transformation is constructed between spacelike surfaces of constant negative curvature and timelike surfaces of constant negative curvature in three-dimensional Minkowksi 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 Leibbrandt [J. Math. Phys. 19, (1978)].
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