Logo image
Local structure of ideal knots, ii constant curvature case
Journal article   Peer reviewed

Local structure of ideal knots, ii constant curvature case

Oguz C Durumeric
Journal of Knot Theory and its Ramifications, Vol.18(11), pp.1525-1537
2009
DOI: 10.1142/S0218216509007609

View Online

Abstract

The thickness, NIR (K) of a knot or link K is defined to be the radius of the largest open solid tube one can put around the curve without any self intersections of the normal discs, which is also known as the normal injectivity radius of K. For C 1,1 curves K, [Formula: see text], where κ(K) is the generalized curvature, and the double critical self distance DCSD (K) is the shortest length of the segments perpendicular to K at both end points. The knots and links in ideal shapes (or tight knots or links) belong to the minima of ropelength = length/thickness within a fixed isotopy class. In this article, we prove that NIR (K) = ½ DCSC (K), for every relative minimum K of ropelength in R n for certain dimensions n, including n = 3.

Details

Metrics

Logo image