Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 52, Number 4 (2000), 515-532.
Timelike surfaces with constant mean curvature in Lorentz three-space
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.
Tohoku Math. J. (2), Volume 52, Number 4 (2000), 515-532.
First available in Project Euclid: 3 May 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.tmj/1178207753