The Cauchy-Riemann strain functional for Legendrian curves in the 3-sphere
Differential Geometry
2020-03-05 v1
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.
Keywords
Cite
@article{arxiv.2003.01713,
title = {The Cauchy-Riemann strain functional for Legendrian curves in the 3-sphere},
author = {Emilio Musso and Filippo Salis},
journal= {arXiv preprint arXiv:2003.01713},
year = {2020}
}
Comments
37 pages, 10 figures, to appear in "Annali di Matematica Pura ed Applicata"