The Cauchy-Riemann strain functional for Legendrian curves in the 3-sphere

2020/03/03 by Musso, Emilio, Salis, Filippo · 1 citation
#32V05 #37K10 #37K25 #53A20 #53D20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.01713

Abstract

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 investigated. 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 phenomenological invariants is given.

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