In this paper, we obtain some relationships between the curvatures of (r + 1)-dimensional generalized time-like ruled surfaces. We also calculate the drall of a generalized time-like ruled surfaces when the base curve is taken as an orthogonal trajectory of the generated spaces.

Recent research has produced results on subdivision in arbitrary manifolds. These results can be applied to the manifold of lines and thus we can create subdivision schemes especially for ruled surfaces. We present different methods for refining discrete models of ruled surfaces: An algorithm combining subdivision and projection to the manifold of lines in Euclidean three-space. A further algor...

The object of this paper is to investigate the properties ruled surface which direction vector has a constant slope with osculator plane base curve in Galiean $3-$space. We obtain some kind by calculating geometric invariants. Also, we give an application on example and their graphs are visualized using Mathematica program.

A non-linear differential equation is analyzed to determine the geodesic curves on ruled surfaces with time-like rulings inR31. When it is assumed that curvature and torsion of the base curve and components with respect to Frenet’s frame of time-like straight-line are constants, for a special integration constant, it appears that the resulting non-linear differential equation can be integrated ...