Positive isotropic curvature and self-duality in dimension 4

Thomas Richard; Harish Seshadri

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arXiv · 1311.5256

Positive isotropic curvature and self-duality in dimension 4

Thomas Richard·Harish Seshadri

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Abstract

We study a positivity condition for the curvature of oriented Riemannian 4-manifolds: The half-$PIC$ condition. It is a slight weakening of the positive isotropic curvature ($PIC$) condition introduced by M. Micallef and J. Moore. We observe that the half-$PIC$ condition is preserved by the Ricci flow and satisfies a maximality property among all Ricci flow invariant positivity conditions on the curvature of oriented 4-manifolds. We also study some geometric and topological aspects of half-$PIC$ manifolds.

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Thomas Richard, Harish Seshadri. 2014-01-29. Positive isotropic curvature and self-duality in dimension 4. https://arxiv.org/abs/1311.5256

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