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Positive isotropic curvature and self-duality in dimension 4

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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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Authors and Affiliations

  1. Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), UPEM, UPEC, CNRS, Université Paris-Est, 94010, Créteil, France

    Thomas Richard

  2. Mathematics Department, Indian Institute of Science, Bangalore, 560012, India

    Harish Seshadri

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  1. Thomas Richard
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  2. Harish Seshadri
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Correspondence to Thomas Richard.

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Richard, T., Seshadri, H. Positive isotropic curvature and self-duality in dimension 4. manuscripta math. 149, 443–457 (2016). https://doi.org/10.1007/s00229-015-0790-2

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