The lower-order cr-invariant variational problem for Legendrian curves in the 3-sphere is studied, and its Euler–Lagrange equations are deduced. Closed critical curves are investi- gated. Closed critical curves with non-constant cr-curvature are characterized. We prove that their cr-equivalence classes are in one-to-one correspondence with the rational points of a connected planar domain. A procedure to explicitly build all such curves is described. In addition, a geometrical interpretation of the rational parameters in terms of three phe- nomenological invariants is given.
The Cauchy–Riemann strain functional for Legendrian curves in the 3-sphere / Musso, Emilio; Salis, Filippo. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - (2020), pp. 1-40.
Titolo: | The Cauchy–Riemann strain functional for Legendrian curves in the 3-sphere |
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Data di pubblicazione: | 2020 |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10231-020-00974-7 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/11583/2803032