Oberseminar: Kazuko Matsumoto (G.15.25)
Let S be a non-singular complex curve in ℂℙ² and let δₛ 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 δₛ. 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 ℂℙ².
