On the scalar curvature of self-dual manifolds
type: Item
instance of: scholarly article
title: On the scalar curvature of self-dual manifolds
zbMATH Open document ID: 0789.53025
DOI: 10.1007/BF01459499
author: Jongsu Kim
published in: Mathematische Annalen
publication date: 1994-06-22T00:00:00Z
full work available at URL: https://eudml.org/doc/165129
review text: We generalize LeBrun's explicit ``hyperbolic ansatz'' construction of self-dual metrics on connected sums of conformally flat manifolds and \(\mathbb{C} P^ 2\)'s through a systematic use of the theory of hyperbolic geometry and Kleinian groups. (This construction produces [\textit{C. LeBrun}, Self-dual manifolds and hyperbolic geometry, Lect. Notes Pure Appl. Math. 145, 99-131 (1993)], for example, all self-dual manifolds with semi-free \(S^ 1\)-action and with either nonnegative scalar curvature or positive-definite intersection form.) We then point out a simple criterion for determining the sign of the scalar curvature of these conformal metrics. Exploiting this, we then show that the sign of the scalar curvature can change on connected components of the moduli space of self-dual metrics, thereby answering a question raised by \textit{A. A. King} and \textit{D. Kotschick} [Math. Ann. 294, 591-609 (1992; Zbl 0765.58005)].
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 30F40
zbMATH DE Number: 537346
zbMATH Keywords: connected sums
zbMATH Keywords: conformally flat manifolds
zbMATH Keywords: Kleinian groups
zbMATH Keywords: conformal metrics
MaRDI profile type: Publication
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Wikidata QID: Q125705664
description: scientific article; zbMATH DE number 537346