A compactness theorem for locally homogeneous spaces

Francesco Pediconi

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arXiv · 1911.05062

A compactness theorem for locally homogeneous spaces

Francesco Pediconi

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Abstract

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

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Francesco Pediconi. 2019-11-12. A compactness theorem for locally homogeneous spaces. https://arxiv.org/abs/1911.05062

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