LIGHTLIKE RULED AND REVOLUTION SURFACES IN �����3 1

Abstract

In this paper lightlike ruled surfaces in 􀔹3 1=(􀔹3,-dx2+dy2+dz2) are studied with respect to whetherruling curves are spacelike or null. It is seen that, in the first case the Gaussian curvature of the ruled surfacesvanishes. In the second case the Gaussian curvature of the ruled surfaces are negative. In the second caselightlike ruled surfaces are totally umbilical. Furthermore, lightlike surfaces of revolution are shown to beonly cones, and the second type lightlike ruled surface.