Diverging sequences of unit volume invariant metrics with bounded curvature

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.