Parallel curves in Minkowski 3-space

Gumushane University Journal of Science, vol.12, no.2, pp.480-486, 2022 (TRDizin)

For a curve  on the plane, there exists the curve  at a fixed distance r (except for some degenerate cases). The curve

 can be alternatively produced as an envelope of circles with the radius r moving along the curve  . As a result,

when this structure is translated to three-dimensional space two parallel curves are obtained. In this study defining some

time-like parallel curves on 3-dimensional Minkowski space, some important theorems about these are stated and proved.