Diverging sequences of unit volume invariant metrics with bounded curvature

Abstract

We study 1-parameter families in the space ${\mathcal{M}}_1^G$ 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 ${\mathcal{M}}_1^G$, and we prove some structure results for those which have bounded curvature. We also relate our results to an algebraic version of collapse.

27 pages. Some minor modifications. Accepted for publication in Ann. Global Anal. Geom