Metrics with nonnegative isotropic curvature
type: Item
instance of: scholarly article
title: Metrics with nonnegative isotropic curvature
zbMATH Open document ID: 0804.53058
DOI: 10.1215/S0012-7094-93-07224-9
author: Mario J. Micallef
author: McKenzie Y. Wang
published in: Duke Mathematical Journal
publication date: 1995-01-22T00:00:00Z
review text: The notion of positive isotropic curvature generalizes classical curvature conditions such as strict pointwise quarter pinching and positive curvature operator. Among the results obtained is the following theorem. If \((M^{2n},g)\) is an even-dimensional closed Riemannian manifold, then (a) \(b_ 2(M)= 0\) if \(g\) has positive isotropic curvature, and (b) if \(g\) is locally irreducible, has nonnegative isotropic curvature, and \(b_ 2(M)\neq 0\), then \(b_ 2(M)= 1\) and \((M,g)\) is Kähler with positive first Chern class. The paper concludes with results on four-manifolds with nonnegative isotropic curvature.
reviewed by: A. P. Stone
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 559006
zbMATH Keywords: Kähler manifold
zbMATH Keywords: positive isotropic curvature
zbMATH Keywords: Chern class
MaRDI profile type: Publication
cites work: Sur quelques variétés riemanniennes suffisamment pincées
cites work: Q3270944
cites work: Q5593748
cites work: Sur quelques variétés d'Einstein compactes
cites work: Q4720334
cites work: Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein
cites work: Q3041921
cites work: Holomorphic bisectional curvature
cites work: The classification of simply connected manifolds of positive scalar curvature
cites work: Three-manifolds with positive Ricci curvature
cites work: Four-manifolds with positive curvature operator
cites work: Q3897665
cites work: Compact four-dimensional Einstein manifolds
cites work: On compact Kähler manifolds with positive definite Ricci tensor
cites work: Q5565587
cites work: Q3995493
cites work: On the Topology of Self-Dual 4-Manifolds
cites work: Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes
cites work: The second variation of area of minimal surfaces in four-manifolds
cites work: Q3772865
cites work: De nouvelles formules de Weitzenböck pour des endomorphismes harmoniques. Applications géométriques
cites work: On the structure of manifolds with positive scalar curvature
cites work: Conformally flat manifolds, Kleinian groups and scalar curvature
cites work: On Manifolds with Nonnegative Curvature on Totally Isotropic 2-Planes
cites work: On Calabi's conjecture for complex surfaces with positive first Chern class
cites work: The Cohomology of Homogeneous Spaces
cites work: On the curvature of compact Hermitian manifolds
cites work: On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
full work available at URL: s0012-7094-93-07224-9
OpenAlex ID: W2039799029
description: scientific article; zbMATH DE number 559006