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Curvature invariants, differential operators and local homogeneity |
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| Authors: | Friedbert Prü fer Franco Tricerri Lieven Vanhecke |
| Affiliation: | Universität Leipzig, Fakultät für Mathematik und Informatik, Mathematisches Institut, Augustusplatz 10, D-04109, Leipzig, Germany ; Universität Leipzig, Fakultät für Mathematik und Informatik, Mathematisches Institut, Augustusplatz 10, D-04109, Leipzig, Germany Lieven Vanhecke ; Katholieke Universiteit Leuven, Departement of Mathematics, Celestijnenlaan 200B, B-3001 Leuven, Belgium |
| Abstract: | We first prove that a Riemannian manifold  with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold  whose Laplacian commutes with all invariant differential operators is a locally homogeneous space. |
| Keywords: | Curvature invariants locally homogeneous spaces Laplacian invariant differential operators commutativity spaces with volume-preserving geodesic symmetries |
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