Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

A REMARK CONCERNING UNIVERSAL CURVATURE IDENTITIES ON 4-DIMENSIONAL RIEMANNIAN MANIFOLDS

  • Received : 2011.06.29
  • Published : 2012.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

We shall prove the universality of the curvature identity for the 4-dimensional Riemannian manifold using a different method than that used by Gilkey, Park, and Sekigawa [5].

Keywords

References

  1. M. Berger, Quelques formules de variation pour une structure riemannienne, Ann. Sci. Ecole Norm. Sup. 4 3 (1970), 285-294. https://doi.org/10.24033/asens.1194
  2. Y. Euh, J. H. Park, and K. Sekigawa, A Curvature identity on a 4-dimensional Riemannian manifold, Results. Math., in press, doi 10.1007/s00025-011-0164-3.
  3. Y. Euh, J. H. Park, and K. Sekigawa, A generalization of a 4-dimensional Einstein manifold, to appear Mathematica Slovaca.
  4. Y. Euh, J. H. Park, and K. Sekigawa, Critical metrics for squared-norm functionals of the curvature on 4-dimensional manifolds, Differential Geom. Appl. 29 (2011), no. 5, 642-646. https://doi.org/10.1016/j.difgeo.2011.07.001
  5. P. Gilkey, J. H. Park, and K. Sekigawa, Universal curvature identities, Differential Geom. Appl. 29 (2011), no. 6, 770-778. https://doi.org/10.1016/j.difgeo.2011.08.005
  6. P. Gilkey, J. H. Park, and K. Sekigawa, The spanning set, unpublished.
  7. M.-L. Labbi, Variational properties of the Gauss-Bonnet curvatures, Calc. Var. Partial Differential Equations 32 (2008), no. 2, 175-189. https://doi.org/10.1007/s00526-007-0135-4
  8. M.-L. Labbi, On generalized Einstein metrics, Balkan J. Geom. Appl. 15 (2010), no. 2, 69-77.
  9. E. Puffini, Curvature identities, unpublished.
  10. H. Weyl, Reine Infinitesimalgeometrie, Math. Z. 2 (1918), no. 3-4, 384-411. https://doi.org/10.1007/BF01199420

Cited by

  1. Transplanting geometrical structures vol.31, pp.3, 2013, https://doi.org/10.1016/j.difgeo.2013.03.006