On the curvature of biquotients

TL;DR

This paper investigates the curvature properties of biquotients and related manifolds, aiming to deepen understanding of manifolds with positive or non-negative curvature through specific examples and constructions.

Contribution

It analyzes the curvature of Eschenburg and Bazaikin biquotients and torus quotients of S^3 x S^3, providing new insights into their geometric structures.

Findings

Identification of curvature properties of specific biquotients

Examples of manifolds with positive or non-negative curvature

Enhanced understanding of curvature behavior in biquotients

Abstract

As a means to better understanding manifolds with positive curvature, there has been much recent interest in the study of non-negatively curved manifolds which contain either a point or an open dense set of points at which all 2-planes have positive curvature. We study infinite families of biquotients defined by Eschenburg and Bazaikin from this viewpoint, together with torus quotients of $S^3 \x S^3$.