Curvature invariants, Killing vector fields, connections and cohomogeneity
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- by Sergio Console and Carlos Olmos PDF
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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.References
- J. Bičák and V. Pravda, Curvature invariants in type-$N$ spacetimes, Classical Quantum Gravity 15 (1998), no. 6, 1539–1555. MR 1627964, DOI 10.1088/0264-9381/15/6/011
- Matthias Blau, José Figueroa-O’Farrill, and George Papadopoulos, Penrose limits, supergravity and brane dynamics, Classical Quantum Gravity 19 (2002), no. 18, 4753–4805. MR 1939801, DOI 10.1088/0264-9381/19/18/310
- Alan Coley, Sigbjørn Hervik, and Nicos Pelavas, On spacetimes with constant scalar invariants, Classical Quantum Gravity 23 (2006), no. 9, 3053–3074. MR 2220874, DOI 10.1088/0264-9381/23/9/018
- Sergio Console and Carlos Olmos, Level sets of scalar Weyl invariants and cohomogeneity, Trans. Amer. Math. Soc. 360 (2008), no. 2, 629–641. MR 2346465, DOI 10.1090/S0002-9947-07-04529-1
- D. B. A. Epstein, Natural tensors on Riemannian manifolds, J. Differential Geometry 10 (1975), no. 4, 631–645. MR 415531
- Bertram Kostant, Holonomy and the Lie algebra of infinitesimal motions of a Riemannian manifold, Trans. Amer. Math. Soc. 80 (1955), 528–542. MR 84825, DOI 10.1090/S0002-9947-1955-0084825-8
- Andreas Koutras and Colin McIntosh, A metric with no symmetries or invariants, Classical Quantum Gravity 13 (1996), no. 5, L47–L49. MR 1390083, DOI 10.1088/0264-9381/13/5/002
- 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, DOI 10.1007/BF00128003
- 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).
- Friedbert Prüfer, Franco Tricerri, and Lieven Vanhecke, Curvature invariants, differential operators and local homogeneity, Trans. Amer. Math. Soc. 348 (1996), no. 11, 4643–4652. MR 1363946, DOI 10.1090/S0002-9947-96-01686-8
- I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685–697. MR 131248, DOI 10.1002/cpa.3160130408
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
- MR Author ID: 270951
- Email: olmos@mate.uncor.edu
- 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
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 1069-1072
- MSC (2000): Primary 53C30; Secondary 53C21
- DOI: https://doi.org/10.1090/S0002-9939-08-09669-X
- MathSciNet review: 2457448