Ricci-Positive Metrics on Connected Sums of Projective Spaces
Differential Geometry
2019-01-14 v3 Geometric Topology
Abstract
It is a well known result of Gromov that all manifolds of a given dimension with positive sectional curvature are subject to a universal bound on the sum of their Betti numbers. On the other hand, there is no such bound for manifolds with positive Ricci curvature: indeed, Perelman constructed positive Ricci metrics on arbitrary connected sums of complex projective planes. In this paper, we revisit and extend Perelman's techniques to construct positive Ricci metrics on arbitrary connected sums of complex, quaternionic, and octonionic projective spaces in every dimension.
Keywords
Cite
@article{arxiv.1705.05055,
title = {Ricci-Positive Metrics on Connected Sums of Projective Spaces},
author = {Bradley Lewis Burdick},
journal= {arXiv preprint arXiv:1705.05055},
year = {2019}
}
Comments
Final Version. 25 pages, 11 figures. Accepted for publication in Differential Geometry and its Applications. See author's webpage for technical appendices