# On the Smarandache Curves of Spatial Quaternionic Involute Curve

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## Abstract

In this study, the spatial quaternionic curve and the relationship between Frenet frames of involute curve of spatial quaternionic curve are expressed by using the angle between the Darboux vector and binormal vector of the basic curve. Secondly, the Frenet vectors of involute curve are taken as position vector and curvature and torsion of obtained Smarandache curves are calculated. The calculated curvatures and torsions are given depending on Frenet apparatus of basic curve. Finally, an example is given and the shapes of these curves are drawn by using Mapple program.

## Keywords

Quaternionic curves Involute curve Quaternionic Smarandache curves## Mathematics Subject Classification

53A04 53C26## Notes

### Acknowledgements

Authors are also thankful to honorable reviewers for their valuable suggestion which helps to improve the quality of the manuscript.

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© The National Academy of Sciences, India 2019