The signature of Kähler surfaces immersed into \({\mathbb{C}}P^ m\)
type: Item
instance of: scholarly article
title: The signature of Kähler surfaces immersed into \({\mathbb{C}}P^ m\)
zbMATH Open document ID: 0651.53039
author: Domenico Perrone
published in: Tokyo Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: 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 \(M={\mathbb{C}}P^ 1(1)\times {\mathbb{C}}P^ 1(1).\)
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 4062096
zbMATH Keywords: compact Kähler surface
zbMATH Keywords: complex projective space
zbMATH Keywords: signature
zbMATH Keywords: curvature
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270134267
OpenAlex ID: W2077486047
DOI: 10.3836/TJM/1270134267
description: scientific article; zbMATH DE number 4062096