Legendrians with vanishing Shelukhin-Chekanov-Hofer metric
arXiv:2301.07575 · doi:10.4310/ARKIV.2024.v62.n1.a8
Abstract
We show that the Legendrian lift of an exact, displaceable Lagrangian has vanishing Shelukhin-Chekanov-Hofer pseudo-metric by lifting an argument due to Sikorav to the contactization. In particular, this proves the existence of such Legendrians, providing counterexamples to a conjecture of Rosen and Zhang.
3 pages; minor revision, added a brief comparison to a similar result by Cant; accepted for publication in Arkiv för Matematik