Canal Surface Around A Spacelike Focal Curve In Lorentz 3-Space

Abstract

In this paper, we study the tubular surface around a spacelike focal curve in Lorentz 3-Space. First for better understanding of the subject, the definitions and equations of the canal surface around a regular curve in 3-dimensional Euclidean space are given. Section 3, concerned with some important definitions and theorems about focal curves in 3-dimensional Lorentz space. In section 4, we derive equations for canal and tubular surfaces around a spacelike focal curve in 3-dimensional Lorentz. Then we obtain the first and the second fundamental forms on the tubular surfaces in the same space. Gauss and mean curvatures of this surface are obtained. Finally, in this space it is investigated if the parameter curves for the tubular surface are geodesic or asymptotic and related theorems about them are stated and proved.