We investigate the problem of -loops, namely closed curves in the three-dimensional Euclidean space, with prescribed curvature and torsion . In particular we focus on some perturbative cases, taking and with and converging to the constants 1 and 0, respectively, as . We prove existence of branches of -loops (for small ) emanating from circles which correspond to stable zeroes of a suitable vector field .
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Paolo Caldiroli, Michela Guida, Closed curves in <strong>R</strong><sup>3</sup> with prescribed curvature and torsion in perturbative cases — Part 2: Sufficient conditions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 4, pp. 291–307DOI 10.4171/RLM/470