On the Module of Relatively Exact 1-Forms

Hossein Movasati

Keywords: Integrable foliation - meromorphic 1-form - holonomy

Let $\F$ be a foliation in $\pro$ with a noncomposite first integral $g$ and let $\omega_1$ be a relatively exact meromorphic 1-form modulo $\F$. We prove that if every $g$-fiber is connected and every $\F$-invariant component of the pole divisor of $\omega_1$ \ is an irreducible $g$-fiber then $\omega_1$ is of the form $df+\omega$ , where $f$ is a meromorphic function on $\pro$ and $\omega$ is a meromorphic 1-form which induces the foliation $\F$.

Anexos:

• te2.ps