JournalsaihpcVol. 1, No. 5pp. 351–359

Uniqueness and non-existence of metrics with prescribed Ricci curvature

  • Dennis M. DeTurck

    University of Pennsylvania
  • Norihito Koiso

    Osaka University
Uniqueness and non-existence of metrics with prescribed Ricci curvature cover
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Abstract

We investigate whether the Ricci tensor uniquely determines the Riemannian structure, and we give conditions that a doubly covariant tensor has to satisfy in order to be the Ricci tensor for some Riemannian structure.

Résumé

Nous cherchons si le tenseur de Ricci détermine la structure riemannienne, et nous donnons des conditions que doit satisfaire un tenseur deux fois covariant pour être le tenseur de Ricci d’une certaine structure riemannienne.

Cite this article

Dennis M. DeTurck, Norihito Koiso, Uniqueness and non-existence of metrics with prescribed Ricci curvature. Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), no. 5, pp. 351–359

DOI 10.1016/S0294-1449(16)30417-6