Mathematische Annalen

, Volume 279, Issue 2, pp 253–265

Scalar curvature of a metric with unit volume

  • Osamu Kobayashi
Article

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References

  1. 1.
    Aubin, T.: The scalar curvature, differential geometry and relativity. M. Cahen, M. Flato (eds.) pp. 5–18. Dordrecht: Reidel 1976Google Scholar
  2. 2.
    Aubin, T.: Nonlinear analysis on manifolds, Monge-Ampère equations. Grundlehren der Math. Wissenschaften, Vol. 252. Berlin, Heidelberg, New York: Springer 1982Google Scholar
  3. 3.
    Bérard Bergery, L.: La coubure scalaire des variétés riemanniennes. Lect. Notes Math. 842. Berlin, Heidelberg, New York: Springer 1981, pp. 225–245.Google Scholar
  4. 4.
    Besse, A.L.: Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, Bd. 10. Berlin, Heidelberg, New York: Springer 1987Google Scholar
  5. 5.
    Bourguignon, J.P.: Une stratification de l.espace des structures riemanniennes. Compos. Math.30, 1–41 (1975)Google Scholar
  6. 6.
    Gidas, B., Ni, W.-M., Nirenberg, L.: Symmetry of positive solutions of nonlinear elliptic equations in ℝn. Math. Anal. and Appl. Part A, Adv. Math. Suppl. Studies Vol.7A, 369–402 (1981)Google Scholar
  7. 7.
    Gromov, M.: Volume and bounded cohomology. Publ. Math. IHES56, 213–307 (1983)Google Scholar
  8. 8.
    Gromov, M., Lawson, H.B., Jr.: The classification of simply connected manifolds of positive scalar curvature. Ann. Math.111, 423–434 (1980)Google Scholar
  9. 9.
    Gromov, M., Lawson, H.B., Jr.: Positive scalar curvature and the Dirac operator on complete Riemannian manifolds. Publ. Math. IHES58, 83–196 (1983)Google Scholar
  10. 10.
    Kazdan, J.L.: Prescribing the curvature of a Riemannian manifold. Reg. Conf. Ser. Math.57, (1985)Google Scholar
  11. 11.
    Kazdan, J.L., Warner, F.W.: Prescribing curvatures. Proc. Symp. Pure Math.27, 309–319 (1975)Google Scholar
  12. 12.
    Kazdan, J.L., Warner, F.W.: A direct approach to the determination of Gaussian and scalar curvature functions. Invent. Math.28, 227–230 (1975)Google Scholar
  13. 13.
    Kobayashi, O.: On total conformal curvature. Thesis, Tokyo Metropolitan University, 1985Google Scholar
  14. 14.
    Obata, M.: The conjectures on conformal transformations of Riemannian manifolds. J. Differ. Geom.6, 247–258 (1971)Google Scholar
  15. 15.
    Schoen, R.: Conformal deformation of a Riemannian metric to constant scalar curvature. J. Differ. Geom.20, 479–496 (1984)Google Scholar
  16. 16.
    Schoen, R., Yau, S.T.: On the structure of manifolds with positive scalar curvature. Manuscr. Math.28, 159–183 (1979)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Osamu Kobayashi
    • 1
    • 2
  1. 1.Department of MathematicsKeio UniversityHiyoshi, YokahamaJapan
  2. 2.Max-Planck-Institut für MathematikBonn 3Federal Republic of Germany

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