Metrics with nonnegative isotropic curvature
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.
scientific article; zbMATH DE number 559006
scientific article