Tohoku Mathematical Journal

Timelike surfaces with constant mean curvature in Lorentz three-space

Rafael López

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A cyclic surface in the Lorentz-Minkowski three-space is one that is foliated by circles. We classify all maximal cyclic timelike surfaces in this space, obtaining different families of non-rotational maximal surfaces. When the mean curvature is a non-zero constant, we prove that if the surface is foliated by circles in parallel planes, then it must be rotational. In particular, we obtain all timelike surfaces of revolution with constant mean curvature.

Article information

Tohoku Math. J. (2), Volume 52, Number 4 (2000), 515-532.

First available in Project Euclid: 3 May 2007

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Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53A40: Other special differential geometries 53C50: Lorentz manifolds, manifolds with indefinite metrics


López, Rafael. Timelike surfaces with constant mean curvature in Lorentz three-space. Tohoku Math. J. (2) 52 (2000), no. 4, 515--532. doi:10.2748/tmj/1178207753.

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