On exotic monotone Lagrangian tori in $\mathbb{C}P^2$ and $S^2 \times S^2$

Abstract

In this note, we prove that two constructions of exotic monotone Lagrangian tori, namely the one by Chekanov and Schlenk and the one obtained by the circle bundle construction of Biran are Hamiltonian isotopic in $\mathbb{C}P^2$ and $S^2 \times S^2$.