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
DOI:
https://doi.org/10.1090/S0002-9947-96-01686-8
MathSciNet review:
1363946
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Abstract | References | Similar Articles | Additional Information
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.
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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:
https://doi.org/10.1090/S0002-9947-96-01686-8
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