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The total curvature of knots under second-order infinitesimal bending

Marija S. Najdanović

Faculty of Natural Sciences and Mathematics, University of Priština, Kosovska Mitrovica, Serbia

E-mail Address: marijamath@yahoo.com

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Svetozar R. Rančić

Faculty of Science and Mathematics, University of Niš, Niš, Serbia

E-mail Address: rancicsv@yahoo.com

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Louis H. Kauffman

Department of Mathematics, Statistics and Computer Science, 851 South Morgan Street, University of Illinois at Chicago, Chicago, Illinois 60607-7045, USA

Department of Mechanics and Mathematics, Novosibirsk State University, Novosibirsk, Russia

E-mail Address: kauffman@uic.edu

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, and

Ljubica S. Velimirović

http://orcid.org/0000-0002-0317-4722

Faculty of Science and Mathematics, University of Niš, Niš, Serbia

E-mail Address: vljubica@pmf.ni.ac.rs

Corresponding author.

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https://doi.org/10.1142/S0218216519500056Cited by:5 (Source: Crossref)

Abstract

In this paper, we consider infinitesimal bending of the second-order of curves and knots. The total curvature of the knot during the second-order infinitesimal bending is discussed and expressions for the first and the second variation of the total curvature are given. Some examples aimed to illustrate infinitesimal bending of knots are shown using figures. Colors are used to illustrate curvature values at different points of bent knots and the total curvature is numerically calculated.

Keywords:

AMSC: 53A04, 53C45, 57M25, 57M27, 78A25

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