Intermediate curvatures and highly connected manifolds

Diarmuid Crowley; David Wraith

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arXiv · 1704.07057

Intermediate curvatures and highly connected manifolds

Diarmuid Crowley·David Wraith

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Abstract

We show that after forming a connected sum with a homotopy sphere, all (2j-1)-connected 2j-parallelisable manifolds in dimension 4j+1, j > 0, can be equipped with Riemannian metrics of 2-positive Ricci curvature. The condition of 2-positive Ricci curvature is defined to mean that the sum of the two smallest eigenvalues of the Ricci tensor is positive at every point. This result is a counterpart to a previous result of the authors concerning the existence of positive Ricci curvature on highly connected manifolds in dimensions 4j-1 for j > 1, and in dimensions 4j+1 for j > 0 with torsion-free cohomology.

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Diarmuid Crowley, David Wraith. 2017-04-24. Intermediate curvatures and highly connected manifolds. https://arxiv.org/abs/1704.07057

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