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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Curvature invariants, differential operators
and local homogeneity


Authors: Friedbert Prüfer, Franco Tricerri and Lieven Vanhecke
Journal: Trans. Amer. Math. Soc. 348 (1996), 4643-4652
MSC (1991): Primary 53C20, 53C25, 53C30
MathSciNet review: 1363946
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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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Additional Information

Friedbert Prüfer
Affiliation: Universität Leipzig, Fakultät für Mathematik und Informatik, Mathematisches Institut, Augustusplatz 10, D-04109, Leipzig, Germany
Email: pruefer@mathematik.uni-leipzig.d400.de

Franco Tricerri
Affiliation: Universität Leipzig, Fakultät für Mathematik und Informatik, Mathematisches Institut, Augustusplatz 10, D-04109, Leipzig, Germany

Lieven Vanhecke
Affiliation: Katholieke Universiteit Leuven, Departement of Mathematics, Celestijnenlaan 200B, B-3001 Leuven, Belgium
Email: lieven.vanhecke@wis.kuleuven.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01686-8
PII: S 0002-9947(96)01686-8
Keywords: Curvature invariants, locally homogeneous spaces, Laplacian, invariant differential operators, commutativity, spaces with volume-preserving geodesic symmetries
Received by editor(s): September 26, 1995
Additional Notes: $^{†}$To our deep sorrow F. Tricceri died in an airplane crash in China on the sixth of June 1995. His contribution to this paper was essential.
Article copyright: © Copyright 1996 American Mathematical Society