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Mathematical Methods in the Applied Sciences
Article . 2021 . Peer-reviewed
License: Wiley Online Library User Agreement
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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Article . 2022
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Generalized tubes in pseudo‐Galilean 3‐space: Split semi‐quaternionic representations and an application to magnetic flux tubes

Generalized tubes in pseudo-Galilean 3-space: split semi-quaternionic representations and an application to magnetic flux tubes
Authors: Orhan Oğulcan Tuncer;

Generalized tubes in pseudo‐Galilean 3‐space: Split semi‐quaternionic representations and an application to magnetic flux tubes

Abstract

This paper deals with generalized tube surfaces (GTs) and their geometric properties in pseudo‐Galilean 3‐space. We classify these surfaces into two types. We firstly compute the first and second fundamental forms to investigate geometric properties of a GT. Then, we obtain the condition for such a surface to be minimal and present some results which express the conditions for which parameter curves on a GT are geodesics, asymptotics, or lines of curvature. Furthermore, we show how to form GTs by using split semi‐quaternions or their matrix representations. Finally, as an application, we introduce generalized magnetic flux tubes in pseudo‐Galilean 3‐space and obtain the local magnetic field components of such surfaces. The theory studied in the paper is supported by illustrated examples.

Related Organizations
Keywords

Applications of differential geometry to physics, Differential geometric aspects in kinematics, pseudo-Galilean space, generalized tube surface, split semi-quaternion, Non-Euclidean differential geometry, mean curvature, Gaussian curvature, magnetic flux tube

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
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