We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature | sec | ≤ 1. Moreover, we show that the set of geometric models is compact in the pointed C1,α-topology.
A compactness theorem for locally homogeneous spaces / Pediconi F.. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - STAMPA. - 23:(2022), pp. 339-360. [10.2422/2036-2145.201912_001]
A compactness theorem for locally homogeneous spaces
Pediconi F.
2022
Abstract
We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature | sec | ≤ 1. Moreover, we show that the set of geometric models is compact in the pointed C1,α-topology.
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