In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.

In this study, a kind of generalized involute and evolute curve pair is considered in 4 dimensional semi Euclidean space with 2 index. The curvatures the associated Frenet Frame generalized
 involute-evolute are presented.

In this work, we deal with a classical differential geometry topic in Minkowski space-time. First, we prove that there are no timelike involutes of a time-like evolute. In the light of this result, we observed that involute curve transforms to a time-like curve when evolute is a space-like helix with a time-like principal normal. Then, we investigated relationships among Frenet-Serret apparatus...

In this paper, the invariants of Smarandache curves, which consist Frenet vectors involute curve, are calculated in terms evolute curve.

The goal of this paper is to characterize the evolute, involute and parallel curves a Bezier curve which applicable computer graphics related subjects. Especially, these couples are investigated at endpoints. Moreover, curvatures given.

This paper concentrates on the requirements of being an integral curve for geodesic spray natural lift curves spherical indicatrices timelike-spacelike involute-evolute pair in Lorentz 3-space. In addition, obtained results were supported by one example.

in this study, a generalization of the theory of involute-evolute curves is presented for ruledsurfaces based on line geometry. using lines instead of points, two ruled surfaces which are offset in the senseof involute-evolute are defined. moreover, the found results are clarified using computer-aided examples