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Level sets of scalar Weyl invariants and cohomogeneity
Author(s):
Sergio
Console;
Carlos
Olmos
Journal:
Trans. Amer. Math. Soc.
360
(2008),
629-641.
MSC (2000):
Primary 53C30;
Secondary 53C21
Posted:
September 21, 2007
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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.
References:
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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:
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
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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