Unknottedness of real Lagrangian tori in $S^2\times S^2$

Abstract

We prove the Hamiltonian unknottedness of real Lagrangian tori in the monotone S 2 ˆS2 , namely any real Lagrangian torus in S 2 ˆS2 is Hamiltonian isotopic to the Clifford torus TClif. The proof is based on a neck-stretching argument, Gromov's foliation theorem, and the Cieliebak-Schwingenheuer criterion.