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arXiv · 2107.07852

A primer on the differential geometry of quaternionic curves

Sergio Giardino
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Abstract

This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic curve are accordingly determined. This new formulation takes benefit of the quaternionic structure and the results are much simpler than the present formulations of quaternionic curves.

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Sergio Giardino. 2021-07-16. A primer on the differential geometry of quaternionic curves. https://doi.org/10.1002/mma.7709

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