Geometric formality of homogeneous spaces and of biquotients

TL;DR

This paper explores the geometric formality of certain homogeneous spaces and biquotients, providing new examples and extending obstructions to formality beyond previously known cases.

Contribution

It introduces new examples of homogeneous spaces with invariant metrics that are geometrically formal and extends obstructions to geometric formality to broader classes.

Findings

Identified homogeneous spaces that are geometrically formal without being symmetric spaces or cohomology spheres.

Extended obstructions to geometric formality to new classes of spaces and biquotients.

Provided examples of sphere bundles with geometric formality properties.

Abstract

We provide examples of homogeneous spaces which are neither symmetric spaces nor real cohomology spheres, yet have the property that every invariant metric is geometrically formal. We also extend the known obstructions to geometric formality to some new classes of homogeneous spaces and of biquotients, and to certain sphere bundles.