# Diverging sequences of unit volume invariant metrics with bounded curvature

## TL;DR

This paper investigates diverging sequences of $G$-invariant, unit volume metrics on homogeneous spaces with bounded curvature, revealing structural insights and connections to algebraic collapse phenomena.

## Contribution

It provides new structure results for diverging metric sequences with bounded curvature on homogeneous spaces, linking geometric divergence to algebraic collapse.

## Key findings

- Characterization of diverging sequences with bounded curvature
- Structural results for such sequences
- Relation to algebraic collapse phenomena

## Abstract

We study 1-parameter families in the space $\mathscr{M}^G_1$ of $G$-invariant, unit volume metrics on a given compact, connected, almost-effective homogeneous space $M=G/H$. In particular, we focus on diverging sequences, i.e. which are not contained in any compact subset of $\mathscr{M}^G_1$, and we prove some structure results for those which have bounded curvature. We also relate our results to an algebraic version of collapse.