Intermediate curvatures and highly connected manifolds
Abstract
We show that after forming a connected sum with a homotopy sphere, all (2j1)connected 2jparallelisable manifolds in dimension 4j+1, j > 0, can be equipped with Riemannian metrics of 2positive Ricci curvature. The condition of 2positive 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 4j1 for j > 1, and in dimensions 4j+1 for j > 0 with torsionfree cohomology.
 Publication:

arXiv eprints
 Pub Date:
 April 2017
 DOI:
 10.48550/arXiv.1704.07057
 arXiv:
 arXiv:1704.07057
 Bibcode:
 2017arXiv170407057C
 Keywords:

 Mathematics  Differential Geometry;
 53C20;
 57R65
 EPrint:
 The current version of the paper proposes the same main results as the previous version, which was withdrawn, but the method of proof is completely new