The total curvature of knots under second-order infinitesimal bending-Reference-Cited by-同舟云学术

The total curvature of knots under second-order infinitesimal bending

Published:2019-01 Issue:01 Volume:28 Page:1950005
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Najdanović Marija S.¹,Rančić Svetozar R.²,Kauffman Louis H.³⁴,Velimirović Ljubica S.²^ORCID

Affiliation:

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

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

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

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

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216519500056

Reference15 articles.

1. Curvature and torsion of the tight closed trefoil knot

2. Total curvature and packing of knots

3. Sur la courbure totale d'une courbe gauche faisant un nœud

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