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Curvature invariants, Killing vector fields, connections and cohomogeneity
Author(s):
Sergio
Console;
Carlos
Olmos
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1069-1072.
MSC (2000):
Primary 53C30;
Secondary 53C21
Posted:
October 2, 2008
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Additional information
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.
References:
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- A. Coley, S. Hervik and N. Pelavas, On spacetimes with constant scalar invariants, Class. Quantum Grav. 23 (2006), 3053-3074. MR 2220874 (2007c:53093)
- 4.
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- 7.
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- 8.
- L. Nicolodi and F. Tricerri, On two theorems of I. M. Singer about homogeneous spaces, Ann. Global Anal. Geom. 8 (1990), no. 2, 193-209. MR 1088511 (92b:53075)
- 9.
- F. Podestà and A. Spiro, Introduzione ai Gruppi di Transformazioni, Volume of the Preprint Series of the Mathematics Department V. Volterra of the University of Ancona (1996).
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- F. Prüfer, F. Tricerri and L. Vanhecke, Curvature invariants, differential operators and local homogeneity, Trans. Amer. Math. Soc. 348, No. 11 (1996), 4643-4652. MR 1363946 (97a:53074)
- 11.
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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/S0002-9939-08-09669-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
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
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