Quasi-positive curvature on Bazaikin spaces

TL;DR

This paper characterizes the sectional curvature of 13-dimensional Bazaikin spaces, showing they all admit quasi-positive curvature and identifying a unique space with almost positive but not positive curvature.

Contribution

It provides a complete curvature classification of Bazaikin spaces and identifies a unique example with almost positive curvature.

Findings

All Bazaikin spaces admit a quasi-positively curved metric.

There is a unique Bazaikin space that is almost positively curved but not positively curved.

Complete characterization of sectional curvature for 13-dimensional Bazaikin spaces.

Abstract

We completely characterize the sectional curvature of all of the $13$-dimensional Bazaikin spaces. In particular, we show that all Bazaikin spaces admit a quasi-positively curved Riemannian metric, and that, up to isometry, there is a unique Bazaikin space which is almost positively curved but not positively curved.