CAUSAL CHARACTERS OF ZERO MEAN CURVATURE SURFACES OF RIEMANN TYPE IN THE LORENTZ-MINKOWSKI 3-SPACE

Abstract

A zero mean curvature surface in the Lorentz-Minkowski 3-space is said to be of Riemann type if it is foliated by circles and at most countably many straight lines in parallel planes. We classify all zero mean curvature surfaces of Riemann type according to their causal characters, and as a corollary, we prove that if a zero mean curvature surface of Riemann type has exactly two causal characters, then the lightlike part of the surface is a part of a straight line.