Curvature invariants, differential operators and local homogeneity

Prüfer, Friedbert; Tricerri, Franco; Vanhecke, Lieven

doi:10.1090/S0002-9947-96-01686-8

Curvature invariants, differential operators and local homogeneity
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by Friedbert Prüfer, Franco Tricerri and Lieven Vanhecke

Trans. Amer. Math. Soc. 348 (1996), 4643-4652

DOI: https://doi.org/10.1090/S0002-9947-96-01686-8

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Abstract:

We first prove that a Riemannian manifold $(M,g)$ with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold $(M,g)$ whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

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