A compactness theorem for locally homogeneous spaces

Abstract

We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature $|\sec |\le 1$. Moreover, we show that the set of geometric models is compact in the pointed ${\mathcal{C}}^{1,\alpha }$-topology.

14 pages. Some minor modifications. Accepted for publication in Ann. Sc. Norm. Super. Pisa Cl. Sci