We study the problem of -loops, namely closed curves in the three-dimensional Euclidean space, with prescribed curvature and torsion . We state a necessary condition for the existence of a bounded sequence of -loops when the functions and converge to the constants 1 and 0, respectively. Moreover we prove some Fredholm-type properties for the ``unperturbed'' problem, with and .
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Paolo Caldiroli, Michela Guida, Closed curves in with prescribed curvature and torsion in perturbative cases. Part 1: Necessary condition and study of the unperturbed problem. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 3, pp. 227–242DOI 10.4171/RLM/466