A curve which is called geodesic on a surface M in Lorentz 3-space is a special curve that its acceleration is everywhere normal to M. In this paper, we analyzed the non-linear differential equation to determine the geodesic curves on ruled surfaces which is obtained by a strictly connected spacelike straight line moving with Frenet’s frame along a timelike curve in . When we assume that curvat...

Let S be a ruled surface inside a smooth 3-fold W. Choose a neighborhood V of S in W and let Ŝ be the formal completion of S in V. Let E be a vector bundle over Ŝ. We show that (under suitable conditions) the local deformation space of E is finite dimensional and smooth. Moreover, we show that E is a flat limit of a flat family of vector bundles whose general element we describe explicitly.