On involute and evolute curves of spacelike curve with a spacelike principal normal in Minkowski 3-space. (English) Zbl 1192.53002

Bukcu, Bahaddin; Karacan, Murat Kemal

Int. J. Math. Comb. 1, 27-37 (2009).

Summary: We generalize the notion of involute and evolute of the space-like curve \(\alpha\) with a space-like principal normal in Minkowski 3-space. Firstly, we show that, the length between the space-like curves \(\alpha\) and \(\beta\) is constant. Furthermore, the Frenet frame of the involute curve \(\beta\) is found as depending on the curvatures of the curve \(\alpha\). We have determined conditions under which the curve \(\alpha\) is planar. Secondly, we find the transformation matrix between the evolute curve \(\beta\) and the curve \(\alpha\). Finally, we compute the curvatures of the evolute curve \(\beta\).

MSC:

53A04	Curves in Euclidean and related spaces
53B30	Local differential geometry of Lorentz metrics, indefinite metrics
53A35	Non-Euclidean differential geometry

Keywords:

space-like curve; involutes; evolutes; Minkowski 3-space