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

 

Level sets of scalar Weyl invariants and cohomogeneity


Authors: Sergio Console and Carlos Olmos
Journal: Trans. Amer. Math. Soc. 360 (2008), 629-641
MSC (2000): Primary 53C30; Secondary 53C21
Published electronically: September 21, 2007
MathSciNet review: 2346465
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Abstract: We prove that the cohomogeneity of a Riemannian manifold coincides locally with the codimension of the foliation by regular level sets of the scalar Weyl invariants.


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Additional Information

Sergio Console
Affiliation: Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy
Email: sergio.console@unito.it

Carlos Olmos
Affiliation: FaMAF, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina
Email: olmos@mate.uncor.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04529-1
PII: S 0002-9947(07)04529-1
Keywords: Homogeneous Riemannian manifolds, Weyl invariants, natural tensors, cohomogeneity
Received by editor(s): July 28, 2005
Published electronically: September 21, 2007
Additional Notes: The first author was partially supported by GNSAGA of INdAM and MIUR (Italy)
The second author was supported by Universidad Nacional de Córdoba and CONICET, and partially supported by Antorchas, ANCyT, Secyt-UNC, and CIEM
Dedicated: To the memory of Aristide Sanini
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.