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A remark on locally homogeneous Riemannian spaces

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Abstract

A locally homogeneous Riemannian space is called non-regular if it is not locally isometric to any globally homogeneous Riemannian space. We show that no non-regular space has non positive Ricci tensor and that a theorem by Alkseevski-Kimelfeld may be extended to the class of locally homogeneous spaces: i.e. any locally homogeneous Riemannian space with zero Ricci tensor is locally euclidean.

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  1. Dipartimento di Matematica “V. Volterra”, Universita’ di Ancona, Via delle Brecce Bianche, 60100, Ancona, Italy

    Andrea Spiro

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  1. Andrea Spiro
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Spiro, A. A remark on locally homogeneous Riemannian spaces. Results. Math. 24, 318–325 (1993). https://doi.org/10.1007/BF03322340

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