Isotropic tori in $\mathbb{C}^m$ revisited

TL;DR

The paper demonstrates the existence of multiple non-Hamiltonian isotopic exact isotropic tori in complex Euclidean spaces, revealing new distinctions in symplectic topology.

Contribution

It establishes the existence of at least two non-Hamiltonian isotopic exact isotropic tori in $\

Findings

Existence of at least two non-Hamiltonian isotopic exact isotropic tori in $\

Discovery of more non-exact isotropic tori in $\

Differentiation between smooth isotopy and Hamiltonian isotopy in isotropic tori.

Abstract

We show that for $m>n\geq 2$, there are at least two exact isotropic $n$-tori in $\mathbb{C}^m$ which are not Hamiltonian isotopic in $\mathbb{C}^m$, even though they are smoothly isotopic as isotropic $n$-tori. We apply this discovery to obtain more distinct non-exact isotropic tori in $\mathbb{C}^m$.