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

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