Examples of projective manifolds not admitting Kähler metric with constant scalar curvature
type: Item
instance of: scholarly article
title: Examples of projective manifolds not admitting Kähler metric with constant scalar curvature
zbMATH Open document ID: 0541.53049
author: Jun-ichi Hano
published in: Osaka Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: For \(P^ k=complex\) projective space of (complex) dimension k, \(P^ m\times P^ n\) (\(m\leq n)\) is imbedded in \(P^{mn+m+n}\) by the canonical Segre imbedding. Let \(M_{m,n}\) be a non-singular hyperplane section of \(P^ m\times P^ n\) in \(P^{mn+m+n}\). The author shows: \(M_{m,n}\), \(m<n\), does not admit a Kähler metric with constant scalar curvature; \(M_{m,m}\) admits a homogeneous Einstein-Kähler metric, hence a Kähler metric with constant scalar curvature.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53B35
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 3859937
zbMATH Keywords: complex projective space
zbMATH Keywords: Kähler metric
zbMATH Keywords: constant scalar curvature
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3859937