Differential geometry using quaternions

Fuente: arXiv
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Autor principal: Giardino, Sergio
Formato: Preprint
Publicado: 2024
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author Giardino, Sergio
author_facet Giardino, Sergio
contents This paper establishes the basis of the quaternionic differential geometry ($\mathbbm H$DG) 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 is 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.
format Preprint
id arxiv_https___arxiv_org_abs_2404_03765
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Differential geometry using quaternions
Giardino, Sergio
Differential Geometry
Mathematical Physics
This paper establishes the basis of the quaternionic differential geometry ($\mathbbm H$DG) 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 is 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.
title Differential geometry using quaternions
topic Differential Geometry
Mathematical Physics
url https://arxiv.org/abs/2404.03765