Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CRITICAL POINTS AND CONFORMALLY FLAT METRICS

  • Published : 2000.08.01
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Abstract

It has been conjectured that, on a compact 3-dimensional manifold, a critical point of the total scalar curvature functional restricted to the space of constant scalar curvature metrics of volume 1 is Einstein. In this paper we find a sufficient condition that a critical point is Einstein. This condition is equivalent for a critical point ot be conformally flat. Its relationship with the Fisher-Marsden conjecture is also discussed.

Keywords

References

  1. Comparison geometry v.30 Scalar Curvature and Geometrization Conjectures for 3-manifolds Anderson M.T.
  2. Ergebnisse der Mathematik Einstein Manifolds A.L.Besse
  3. to appear in Manuscripta Math. Critical points of the Scalar curvature functionals on the Space of metrics of constant scalar curvature S.Hwang
  4. Exact Solutions of Einstein's Field Equations D.Kramer;H.Stephani;E.Herlt;M.MacCallum
  5. J.Math.Pures Appliquees v.62 Sur la geometrie d'une generalisation de l'equation differentielle d'Obata J.Lafontaine
  6. Minimal varieties in real and complex geometry B.Lawson
  7. J.Math.Soc.Japan v.14 no.3 Certain conditions for a Riemannian manifold to be isometric with a sphere M.Obata
  8. Gen.Rel.and Grav. v.8 no.8 A Simple Proof of the Generalization of Israel's Theorem D.Robinson
  9. Proc.Amer.Math.Soc. v.125 no.3 A note on Fischer-Marsden's conjecture Y.Shen