On the involute and evolute curves of the timelike curve in Minkowski 3-space. (English) Zbl 1138.53019

Bukcu, Bahaddin; Karacan, Murat Kemal

Demonstr. Math. 40, No. 3, 721-732 (2007).

The authors consider the involute and evolute curves of a time-like curve \(\alpha\). They express the Frenet frame of the involute curve \(\beta\) of \(\alpha\) in terms of the curvature and torsion of \(\alpha\). They also obtain the transformation matrix between the Frenet frames of the space-like curve \(\beta\) of a unit speed time-like curve \(\alpha\) and they compute the curvature and torsion of \(\beta\).

Reviewer: Christos Baikoussis (Ioannina)

MSC:

53A40	Other special differential geometries
53B30	Local differential geometry of Lorentz metrics, indefinite metrics

Keywords:

time-like curve; involute; evolute, Minkowski 3-space