Obstruction to prescribed positive Ricci curvature
type: Item
instance of: scholarly article
title: Obstruction to prescribed positive Ricci curvature
zbMATH Open document ID: 0676.53050
published in: Pacific Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: This paper extends to non-compact manifolds the obstruction results of \textit{D. DeTurck} and \textit{N. Koiso} [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 1, 351-359 (1984; Zbl 0556.53026)]. The main result states that a Riemannian metric, with largest eigenvalue of the curvature operator uniformly strictly less than 1, cannot be realized as the Ricci tensor of a complete metric. Calabi's maximum principle [\textit{E. Calabi}, Duke Math. J. 25, 45-56 (1958; Zbl 0079.118)] is a key-tool of the proof.
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4107623
zbMATH Keywords: largest eigenvalue
zbMATH Keywords: curvature operator
zbMATH Keywords: Ricci tensor
zbMATH Keywords: maximum principle
zbMATH Keywords: non-compact manifolds
author: Philippe P. Delanoë
MaRDI profile type: Publication
full work available at URL: pjm.1991.148.11
OpenAlex ID: W2032899502
DOI: 10.2140/PJM.1991.148.11
description: scientific article; zbMATH DE number 4107623