Seminar: Kazuko Matsumoto (G.15.25)
Let $S$ be a non-singular complex curve in $\mathbb{CP}^2$ and let $\delta_S$ be the Fubini-Study distance function to $S$.
In this talk, we present an the exact expression for the Levi form of the function $-\log \delta_S$. This is a refinement of the well-known "Takeuchi's inequality". Furthermore, we also give expressions for the eigenvalues of the Levi form with respect to the Fubini-Study metric and show that they are real analytic functions defined in a neighborhood of $S$ including $S$. This study is motivated by its application to the conjecture for the non-existence of Levi-flat hypersurfaces in $\mathbb{CP}^2$.
