On the curvatures of spacelike circular surfaces

Abstract

In this paper a complete system of invariants is presented to study spacelike circular surfaces with fixed radius. The study of spacelike circular surfaces is simplified to the study of two curves: the Lorentzian spherical indicatrix of the unit normals of circle planes and the spacelike spine curve. Then the geometric meanings of these invariants are used to give corresponding properties of spacelike circular surfaces with classical ruled surfaces. Later, we introduce spacelike roller coaster surfaces as a special class of spacelike circular surfaces.