Cohomogeneity two Bazaikin spaces

TL;DR

This paper investigates the sectional curvature properties of cohomogeneity two Bazaikin spaces, revealing that unlike lower cohomogeneity cases, the set of points with positive curvature does not cover the entire space.

Contribution

It provides a detailed analysis of the curvature distribution in cohomogeneity two Bazaikin spaces, highlighting differences from cohomogeneity one and homogeneous cases.

Findings

Set of points with positive curvature is not full measure in cohomogeneity two cases.

Contrasts with cohomogeneity one and homogeneous Bazaikin spaces.

Uses Wilking's metric construction for analysis.

Abstract

We study the sectional curvature of all of the cohomogeneity two Bazaikin spaces with respect to a Riemannian metric construction due to Wilking. We show that, in contrast to the cohomogeneity one and homogeneous case, for all of the cohomogeneity two examples, the set of points with strictly positive curvature does not have full measure.