WILLMORE ENERGY AND TOTAL NORMALCY OF KNOTS WITH MODIFIED ORTHOGONAL FRAME

Ljubica Velimirovic, Mohammed Jamali, Mohammmad Hasan Shahid, Marija S. Najdanovic, Svetozar R. Rancic

Abstract


It is known that a knot is a closed, self-avoiding curve in 3-dimensional space. In the
present article, we compute the total Normalcy and Willmore energy of knots under first order
infinitesimal bending with modified orthogonal frame. Moreover, four illustrious examples with
figures i.e. Trefoil knot, Figure eight knot, P3Q2 knot and P4Q3 knots, have been discussed
and graphically presented to support the computations for bending parameter ϵ = 0 and ϵ > 0.
Colors are used to illustrate normalcy values and Willmore energies at different points of these
knots under infinitesimal bending.


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