Tohoku Mathematical Journal

Timelike surfaces with constant mean curvature in Lorentz three-space

Rafael López

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Abstract

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

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

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178207753

Digital Object Identifier
doi:10.2748/tmj/1178207753

Mathematical Reviews number (MathSciNet)
MR1793934

Zentralblatt MATH identifier
0981.53051

Subjects
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

Citation

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. https://projecteuclid.org/euclid.tmj/1178207753


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References

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