The signature of Kähler surfaces immersed into \({\mathbb{C}}P^ m\)
Let M be a compact Kähler surface immersed in a complex projective space \({\mathbb{C}}P^ m(1)\) of constant holomorphic sectional curvature 1. The author proves that the signature sign(M) and the scalar curvature \(\rho\) of M satisfy \(32\pi^ 2 sign(M)\geq -\int (\rho-4)(\rho-8)\) with equality if and only if \(M={\mathbb{C}}P^ 2(1)\) or \(M={\mathbb{C}}P^ 1(1)\times {\mathbb{C}}P^ 1(1).\)
scientific article; zbMATH DE number 4062096