Tohoku Mathematical Journal
2000
December
SECOND SERIES VOL. 52, NO. 4

Tohoku Math. J.
52 (2000), 515-532

Title TIMELIKE SURFACES WITH CONSTANT MEAN CURVATURE IN LORENTZ 3-SPACE

Author Rafael López

(Received March 1, 1999, revised November 29, 1999)
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.

2000 Mathematics Subject Classification. Primary 53A10; Secondary 53C42.

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