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La courbure scalaire des variétés riemanniennes

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Séminaire Bourbaki vol. 1979/80 Exposés 543 – 560

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Bibliographie

  1. M.F. ATIYAH and I.M. SINGER-The index of elliptic operators I, Ann. of Math. 87 (1968), 484–530; III Ann. of Math. 87 (1968), 546–604; IV Ann. of Math. 92 (1970), 119–138; V Ann. of Math. 92 (1970), 139–149.

    Article  MATH  MathSciNet  Google Scholar 

  2. T. AUBIN-Métriques riemanniennes et courbure, J. Diff. Geom. 4 (1970), 383–424.

    MATH  MathSciNet  Google Scholar 

  3. T. AUBIN-Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, J. Math. pures et appl. 55 (1976), 269–296.

    MATH  MathSciNet  Google Scholar 

  4. T. AUBIN-The scalar curvature, in "Differential Geometry and Relativity" (M. Cahen et Flato, Eds), Reidel, Dordrecht (1976), 5–18.

    Google Scholar 

  5. T. AUBIN-Problèmes isopérimétriques et espaces de Sobolev, J. Diff. Geom. 11 (1976), 573–598.

    MATH  MathSciNet  Google Scholar 

  6. T. AUBIN-Meilleures constantes dans le théorème d'inclusion de Sobolev et un théorème de Fredholm non linéaire pour la transformation conforme de la courbure scalaire, J. Funct. Analysis 32 (1979), 148–174.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. AVEZ-Valeur moyenne du scalaire de courbure sur une variété compacte. Applications relativistes. C.R.A.S. 256 (1963), 5271–5273.

    MATH  MathSciNet  Google Scholar 

  8. L. BÉRARD BERGERY-Sur la courbure des métriques riemanniennes invariantes des groupes de Lie et des espaces homogènes, Annales Sc. Ec. Norm. Sup. 11 (1978), 543–576.

    MATH  Google Scholar 

  9. M.S. BERGER-On the conformal equivalence of compact 2-dimensional manifolds, J. Math. Mech. 19 (1969), 13–18.

    MATH  MathSciNet  Google Scholar 

  10. M.S. BERGER-Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds, J. Diff. Geom. 5 (1971), 325–332.

    MATH  Google Scholar 

  11. E. BOMBIERI-Régularité des hypersurfaces minimales. Séminaire Bourbaki 21e année 1968/69-Exposé no 353 (11 pages).

    Google Scholar 

  12. J.P. BOURGUIGNON-Une stratification de l'espace des structures riemanniennes, Compositio Math., 30(1975), 1–41.

    MATH  MathSciNet  Google Scholar 

  13. J.P. BOURGUIGNON-Premières formes de Chern des variétés kählériennes compactes. Séminaire Bourbaki 30e année 1977/78-Exposé no 507 (18 pages).

    Google Scholar 

  14. Première classe de Chern et courbure de Ricci: preuve de la conjecture de Calabi (Séminaire Palaiseau 1978). Astérisque no 58.

    Google Scholar 

  15. J. CHEEGER et D. GROMOLL-The splitting theorem for manifolds of non negative Ricci curvature. J. Diff. Geom. 6 (1971), 119–128.

    MATH  MathSciNet  Google Scholar 

  16. H.I. ELIASSON-On variations of metrics, Math. Scand. 29 (1971), 317–327.

    MathSciNet  Google Scholar 

  17. A.E. FISCHER and J.E. MARSDEN-Deformations of the scalar curvature, Duke Math. J. 42 (1975), 519–547.

    Article  MATH  MathSciNet  Google Scholar 

  18. H. GLUCK-The generalized Minkowski problem in differential geometry in the large, Ann. of Math. 96 (1972), 245–275.

    Article  MATH  MathSciNet  Google Scholar 

  19. M. GROMOV-Stable maps of foliations in manifolds, Izv. Akad. Nauk SSSR, Ser. Mat. Tom 33 (1969), 734 (Math of the USSR-Izvestija 3 (1979) 671).

    MATH  Google Scholar 

  20. M. GROMOV and H.B. LAWSON, Jr.-Spin and scalar curvature in the presence of a fundamental group I, Ann. of Math. 111(1980), 209–230.

    Article  MATH  MathSciNet  Google Scholar 

  21. M. GROMOV and H.B. LAWSON, Jr-The classification of simply connected manifolds of positive scalar curvature (preprint).

    Google Scholar 

  22. F. HIRZEBRUCH-Topological methods in algebraic topology, Springer Verlag, Berlin Heidelberg New-York, (1966).

    Google Scholar 

  23. N. HITCHIN-Harmonic spinors, Adv. in Math. 14 (1974), 1–55.

    Article  MATH  MathSciNet  Google Scholar 

  24. J.L. KAZDAN and F.W. WARNER-Integrability conditions for Δu=k-keαu` with applications to Riemannian geometry, Bull. A.M.S. 77 (1971), 819–823.

    Article  MATH  MathSciNet  Google Scholar 

  25. J.L. KAZDAN and F.W. WARNER-Curvature functions for 2-manifolds with negative Euler characteristic, Bull. A.M.S. 78 (1972), 570–574.

    MATH  MathSciNet  Google Scholar 

  26. J.L. KAZDAN and F.W. WARNER-Surfaces of revolution with monotonic increasing curvature and an application to the equation u = 1-Ke2u on S2, Proceeding A.M.S. 32 (1972), 139–141.

    Article  MATH  MathSciNet  Google Scholar 

  27. J.L. KAZDAN and F.W. WARNER-Curvature functions for 2-manifolds, Proc. of Symposia in Pure Math. 23 (1973), 387–392.

    MATH  MathSciNet  Google Scholar 

  28. J.L. KAZDAN and F.W. WARNER-Curvature functions for compact 2-manifolds, Ann. of Math. 99 (1974), 14–47.

    Article  MATH  MathSciNet  Google Scholar 

  29. J.L. KAZDAN and F.W. WARNER-Curvature functions for open 2-manifolds, Ann. of Math. 99 (1974), 203–219.

    Article  MATH  MathSciNet  Google Scholar 

  30. J.L. KAZDAN and F.W. WARNER-Scalar curvature and conformal deformation of Riemannian structure, J. Diff. Geom. 10 (1975), 113–134.

    MATH  MathSciNet  Google Scholar 

  31. J.L. KAZDAN and F.W. WARNER-Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures, Ann. of Math. 101 (1975), 317–331.

    Article  MATH  MathSciNet  Google Scholar 

  32. J.L. KAZDAN and F.W. WARNER-Prescribing curvatures, Proc. of Symposia in Pure Math. 27 (1975), 309–319.

    MATH  MathSciNet  Google Scholar 

  33. J.L. KAZDAN and F.W. WARNER-A direct approach to the determination of Gaussian and scalar curvature function, Inventiones Math. 28 (1975), 227–230.

    Article  MATH  MathSciNet  Google Scholar 

  34. D. KOUTROUFIOTIS-On Gaussian curvature and conformal mapping, J. Diff. Geom. 7 (1972), 481–490.

    MathSciNet  Google Scholar 

  35. H.B. LAWSON, Jr and S.T. YAU-Scalar curvature, non-abelian group actions, and the degree of symmetry of exotic spheres, Comm. Math. Helv. 49 (1974), 232–244.

    MATH  MathSciNet  Google Scholar 

  36. L. LEMAIRE-Existence des applications harmoniques et courbure des variétés, Séminaire Bourbaki 32e année 1979/80 Exposé no 553 (21 pages).

    Google Scholar 

  37. A. LICHNEROWICZ-Spineurs harmoniques, C.R.A.S. 257 A (1963), 7–9.

    MathSciNet  Google Scholar 

  38. J. MILNOR-Remarks concerning spin manifolds, "Differential geometry and Combinatorial Topology" Princeton University Press (1965), 55–62.

    Google Scholar 

  39. J. MOSER-A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1971), 1077–1092.

    Article  MATH  Google Scholar 

  40. J. MOSER-On a nonlinear problem in differential geometry, in Dynamical Systems (M. Peixoto ef.) Academic Press, New York, 1973, 273–280.

    Google Scholar 

  41. B. O'NEILL-The fundamental equations of a submersion, Mich. Math. J. 13 (1966), 459–469.

    Article  MATH  MathSciNet  Google Scholar 

  42. R. SCHOEN and S.T. YAU-Incompressible minimal surfaces, three-dimensional manifolds with nonnegative scalar curvature, and the positive mass conjecture in general relativity, Proc. N.A.S. U.S.A. 75 (1978), 2567.

    Article  MATH  MathSciNet  Google Scholar 

  43. R. SCHOEN and S.T. YAU-Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature, Ann. of Math. 110 (1979), 127–142.

    Article  MATH  MathSciNet  Google Scholar 

  44. R. SCHOEN and S.T. YAU-On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), 159–183.

    Article  MATH  MathSciNet  Google Scholar 

  45. R. SCHOEN and S.T. YAU-On the proof of the positive mass conjecture in general relativity, Comm. Math. Phys. 65 (1979), 45–76.

    Article  MATH  MathSciNet  Google Scholar 

  46. M. SPIVAK-A comprehensive introduction to differential geometry, Publish or Perish.

    Google Scholar 

  47. N.S. TRUDINGER-On imbeddings into Orlicz Spaces and some applications, J. Math. Mech. 17 (1967), 473–483.

    MATH  MathSciNet  Google Scholar 

  48. N.S. TRUDINGER-Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa 22 (1968), 265–274.

    MATH  MathSciNet  Google Scholar 

  49. N.R. WALLACH and F.W. WARNER-Curvature forms for 2-manifolds, Proc. A.M.S. 25 (1970) 712–713.

    Article  MATH  MathSciNet  Google Scholar 

  50. H. YAMABE-On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12 (1960), 21–37.

    MATH  MathSciNet  Google Scholar 

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  1. Era no 839 Cnrs Uer de Mathématiques, Université de Nancy I Co 140, 54037, Nancy Cedex

    Lionel Bérard Bergery

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Bergery, L.B. (1981). La courbure scalaire des variétés riemanniennes. In: Séminaire Bourbaki vol. 1979/80 Exposés 543 – 560. Lecture Notes in Mathematics, vol 842. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0089937

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  • DOI: https://doi.org/10.1007/BFb0089937

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