منابع مشابه
Minimal Curves of Constant Torsion
The Griffiths formalism is applied to find constant torsion curves which are extremal for arclength with respect to variations preserving torsion, fixing the endpoints and the binormals at the endpoints. The critical curves are elastic rods of constant torsion, which are shown to not realize certain boundary conditions. In the calculus of variations under nonholonomic constraints, one tries to ...
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The sine-Gordon equation with periodic boundary conditions describes integrable dynamics on the space of closed curves of constant torsion, for which multi-phase solutions provide large classes of canonical knot representatives. In this letter we discuss the use of Bäcklund transformations for studying the topological properties and symmetries of multi-phase solutions and of their homoclinic ma...
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EXAMPLES. (i) The multiplicative group A = Gm is the algebraic group whose points over a field are the nonzero elements of the field. Then for any field K, Tor Gm(K) are the roots of unity contained in K. (ii) A = Gm×Gm then Tor(A) = Tor(Gm)×Tor(Gm) = {(x, y) : x, y ∈ K are roots of unity}. (iii) Let A be an elliptic curve. Over the complex numbers we can uniformize A as A = C/L where L is a la...
متن کاملTorsion Packets on Curves
Let X be a curve of genus g ≥ 2 over a field of characteristic zero. Then X has at most finitely many torsion packets of size greater than 2. Moreover, X has infinitely many torsion packets of size 2 if and only if either g = 2, or g = 3 and X is both hyperelliptic and bielliptic. 1. Raynaud’s theorem Let X be an algebraic curve defined over an algebraically closed field K of characteristic zer...
متن کاملLength Minimization for Space Curves Undernonholonomic Constraints : the Constant Torsion
The Griiths formalism is applied to nd constant torsion curves which are extremal for arclength with respect to variations preserving torsion, xing the endpoints and the binormals at the endpoints. The critical curves are elastic rods of constant torsion, which are shown to not realize certain boundary conditions. In the calculus of variations under nonholonomic constraints, one tries to nd the...
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ژورنال
عنوان ژورنال: Journal of Geometry
سال: 2013
ISSN: 0047-2468,1420-8997
DOI: 10.1007/s00022-013-0166-2