Intermediate curvatures and highly connected manifolds
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.
Cite
@article{arxiv.1704.07057,
title = {Intermediate curvatures and highly connected manifolds},
author = {Diarmuid Crowley and David Wraith},
journal= {arXiv preprint arXiv:1704.07057},
year = {2020}
}
Comments
The current version of the paper proposes the same main results as the previous version, which was withdrawn, but the method of proof is completely new