A primer on the differential geometry of quaternionic curves
Sergio Giardino
TL;DR
This paper develops a simplified differential geometry framework for quaternionic curves, utilizing quaternionic structure to derive Frenet-Serret equations and evolutes, enhancing previous formulations.
Contribution
It introduces a new, simpler formulation of quaternionic curve geometry based on quaternionic structure, with explicit Frenet-Serret equations and evolutes.
Findings
Simpler quaternionic curve formulations
Explicit Frenet-Serret equations for quaternionic curves
Derivation of evolutes and evolvents
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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