Geodesic
Surfaces defined by bending of knots
Filomat, Tome 37 (2023) no. 25, p. 8635

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

We consider the definition of the infinitesimal bending of a curve as a vector parametric equation of a surface defined by two free variables: one of them is free variable u which define curve and another is bending parameter ϵ. In this way, while being bent curve is deformed and moved through the space forming a surface. If infinitesimal bending field is of constant intensity, deformed curves form a ruled surface that represents a ribbon. In particular, we consider surfaces obtain by bending of knots both analytically and graphically. We pay attention to the torus knot and possibility of its infinitesimal bending so that the surface determined by bending is a part of the initial torus.
DOI : 10.2298/FIL2325635R
Classification : 53A04, 53A05, 53C45, 57K10
Keywords: infinitesimal bending, curve, knot, ruled surface, ribbon 
Svetozar R Rančić; Marija S Najdanović; Ljubica S Velimirović. Surfaces defined by bending of knots. Filomat, Tome 37 (2023) no. 25, p. 8635 . doi: 10.2298/FIL2325635R
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     title = {Surfaces defined by bending of knots},
     journal = {Filomat},
     pages = {8635 },
     year = {2023},
     volume = {37},
     number = {25},
     doi = {10.2298/FIL2325635R},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2325635R/}
}
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