A sharp characterization of the smooth 4-sphere in curvature terms
type: Item
instance of: scholarly article
title: A sharp characterization of the smooth 4-sphere in curvature terms
zbMATH Open document ID: 0966.53022
published in: Communications in Analysis and Geometry
publication date: 2001-04-18T00:00:00Z
review text: The weak pinching of a Riemannian manifold is given by the norm of its tracefree curvature operator, appropriately normalized by the scalar curvature to obtain a scale invariant. Using the Ricci flow on the space of metrics, the author gives a simplified version of the original proof outlined in [\textit{C. Margerin}, C.R. Acad.\ Sci., Paris, Sér.~I 303, 877-880 (1986; Zbl 0607.53027)] of the theorem: Any compact 4-manifold admitting a metric of positive scalar curvature which is 1/6-weakly pinched is diffeomorphic either to the 4-sphere \(S^4\), the real projective 4-space, the complex projective plane or the product \(S^1\times S^3\). If it is strictly 1/6-weakly pinched, then we have diffeomorphism to \(S^4\) or the the real projective 4-space.
reviewed by: Eric Boeckx
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 1187449
zbMATH Keywords: weak pinching
zbMATH Keywords: Ricci flow
zbMATH Keywords: sphere theorem
author: Christophe M. Margerin
MaRDI profile type: Publication
full work available at URL: cag.1998.v6.n1.a2
OpenAlex ID: W76325780
DOI: 10.4310/CAG.1998.V6.N1.A2
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description: scientific article; zbMATH DE number 1187449