<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The article deals with the infinitesimal bending theory application to the knots theory. The impact of infinitesimal bending on the torsional energy at torus knots is considered, and the results show that it is not stationary under infinitesimal bending. The torsional energy variation is determined as well. We prove that there is no infinitesimal bending field that leaves torus curves on the torus. Besides, we define an infinitesimal bending field that does not tear the torus knots while bending. Having in mind the importance of visualization in the infinitesimal bending theory, we observed infinitesimal bending of a curve in that field using independently developed software. The graphs we obtained are presented in the paper and the torus knots are coloured according to their torsional energy. We calculated the numerical value of torsional energy under infinitesimal bending and, finally, the results are discussed using convenient specific examples.</p>
</abstract>

The article deals with the infinitesimal bending theory application to the knots theory. The impact of infinitesimal bending on the torsional energy at torus knots is considered, and the results show that it is not stationary under infinitesimal bending. The torsional energy variation is determined as well. We prove that there is no infinitesimal bending field that leaves torus curves on the torus. Besides, we define an infinitesimal bending field that does not tear the torus knots while bending. Having in mind the importance of visualization in the infinitesimal bending theory, we observed infinitesimal bending of a curve in that field using independently developed software. The graphs we obtained are presented in the paper and the torus knots are coloured according to their torsional energy. We calculated the numerical value of torsional energy under infinitesimal bending and, finally, the results are discussed using convenient specific examples.

On the torsional energy of torus knots under infinitesimal bending

Department of Mathematics, Faculty of Sciences and Mathematics

University of Priština in Kosovska Mitrovica

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On the torsional energy of torus knots under infinitesimal bending"}

The article deals with the infinitesimal bending theory application to the knots theory. The impact of infinitesimal bending on the torsional energy at torus...

On the torsional energy of torus knots under infinitesimal bending

Published Online: Feb 04, 2023

Page range: 181 - 197

Received: Feb 19, 2022

Accepted: Apr 21, 2022

DOI: https://doi.org/10.2478/auom-2023-0009

Keywords
Infinitesimal bending, torus knots, torsional energy, variation

© 2023 Miroslav D. Maksimović et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the torsional energy of torus knots under infinitesimal bending

Published Online: Feb 04, 2023

Page range: 181 - 197

Received: Feb 19, 2022

Accepted: Apr 21, 2022

DOI: https://doi.org/10.2478/auom-2023-0009

KeywordsInfinitesimal bending, torus knots, torsional energy, variation

© 2023 Miroslav D. Maksimović et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Infinitesimal bending, torus knots, torsional energy, variation