Differential Geometry Using Quaternions

Year 2024, Volume: 17 Issue: 2, 700 - 711, 27.10.2024

Sergio Giardino

https://doi.org/10.36890/iejg.1362006

Abstract

This paper establishes the basis of the quaternionic differential geometry (HDG) initiated in a previous article.
The usual concepts of curves and surfaces are generalized to quaternionic constraints, as well as the curvature and torsion concepts, differential forms, directional derivatives and the structural equations. The analogy between the quaternionic and the real geometries were obtained using a matrix representation of quaternions. The results evidences the quaternionic formalism as a suitable language to differential geometry that can be useful in various directions of future investigation.

Keywords

Curves in Euclidean space, other special differential geometries, quaternion and other division algebras

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