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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Curvature invariants, Killing vector fields, connections and cohomogeneity


Authors: Sergio Console and Carlos Olmos
Journal: Proc. Amer. Math. Soc. 137 (2009), 1069-1072
MSC (2000): Primary 53C30; Secondary 53C21
Published electronically: October 2, 2008
MathSciNet review: 2457448
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Abstract: A direct, bundle-theoretic method for defining and extending local isometries out of curvature data is developed. As a by-product, conceptual direct proofs of a classical result of Singer and a recent result of the authors are derived.


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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/S0002-9939-08-09669-X
PII: S 0002-9939(08)09669-X
Keywords: Homogeneous Riemannian manifolds, Weyl invariants, curvature invariants, Killing vector fields, cohomogeneity
Received by editor(s): April 10, 2008
Published electronically: October 2, 2008
Additional Notes: The first author was partially supported by GNSAGA of INdAM, MIUR of Italy, CONICET, Secyt-UNC and CIEM of Argentina
The second author was supported by Universidad Nacional de Córdoba and CONICET and partially supported by Antorchas, ANCyT, Secyt-UNC and CIEM
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2008 American Mathematical Society