Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | 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 [Enhancements On Off] (What's this?)

  • 1. J. Bičák and V. Pravda, Curvature invariants in type-N spacetimes, Class. Quantum Grav., 15 (1998), no. 6 , 1539-1555 MR 1627964 (99e:83012)
  • 2. M. Blau, J. Figueroa-O'Farrill and G. Papadopoulos, Penrose limits, supergravity and brane dynamics, Class. Quantum Grav. 19 (2002), 4753-4805. MR 1939801 (2003m:83140)
  • 3. 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. S. Console and C. Olmos, Level sets of scalar Weyl invariants and cohomogeneity, Trans. Amer. Math. Soc. 360 (2008), 629-641 MR 2346465
  • 5. D. B. A. Epstein, Natural tensors on Riemannian manifolds, J. Differ. Geom. 10 (1975), 631-645. MR 0415531 (54:3617)
  • 6. B. Kostant, Holonomy and the Lie algebra of infinitesimal motions of a Riemannian manifold, Trans. Amer. Math. Soc. 80 (1955), 528-542. MR 0084825 (18:930a)
  • 7. A. Koutras and C. McIntosh, A metric with no symmetries or invariants, Class. Quantum Grav. 13 (1996), 47-49. MR 1390083 (97g:83027)
  • 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).
  • 10. 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. I.M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685-697. MR 0131248 (24:A1100)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53C30, 53C21

Retrieve articles in all journals with MSC (2000): 53C30, 53C21

Additional Information

Sergio Console
Affiliation: Dipartimento di Matematica Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy

Carlos Olmos
Affiliation: FaMAF, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina

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

American Mathematical Society