Intermediate curvatures and highly connected manifolds

2017/04/24 by Diarmuid Crowley, Crowley, Diarmuid, David C. Wraith +1
Mathematics · Physics and Astronomy · #53C20 #57R65 #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1704.07057

openalex publication_date 2017/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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