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On the involute and evolute curves of the timelike curve in Minkowski 3-space

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Bukcu B. , Karacan K.

Demonstratio Mathematica

2007

tom Vol. 40, nr 3

721-732

In this study, we have generalized the involute and evolute curves of the timelike curve in Minkowski 3-Space. Firstly, we have shown that, the length between the timelike curve alpha and the spacelike curve beta is constant. Furthermore, the Frenet-Serret frame of the involute curve beta has been found as dependent on curvatures of the curve alpha. We have determined the involute curve beta is planar in which conditions. Secondly, we have found transformation matrix between the evolute curve beta and the curve alpha. Finally, we have computed the curvatures of the evolute curve beta.