Homotopies using conformal transformation with invariant total normal twist
AbstractThe aim of this paper is to detect a homotopy to a spherical curve with invariant total normal twist 0. Also, we use conformal transformation to prove a theorem that for any immersed closed C^3 -curve c in the Euclidean 3-space E^3 with vanishing total normal twist, there exists a Frenet curve ĉ homotopic to c in an arbitrary neighborhood of c such that the total normal twist is invariant along the homotopy between c and ĉ in that neighborhood.
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