La courbure scalaire des variétés riemanniennes
Séminaire Bourbaki : vol. 1979/80, exposés 543-560, Séminaire Bourbaki, no. 22 (1981), Exposé no. 556, 21 p.
@incollection{SB_1979-1980__22__225_0,
     author = {B\'erard Bergery, Lionel},
     title = {La courbure scalaire des vari\'et\'es riemanniennes},
     booktitle = {S\'eminaire Bourbaki : vol. 1979/80, expos\'es 543-560},
     series = {S\'eminaire Bourbaki},
     note = {talk:556},
     pages = {225--245},
     publisher = {Springer-Verlag},
     number = {22},
     year = {1981},
     mrnumber = {636526},
     zbl = {0461.53023},
     language = {fr},
     url = {http://archive.numdam.org/item/SB_1979-1980__22__225_0/}
}
TY  - CHAP
AU  - Bérard Bergery, Lionel
TI  - La courbure scalaire des variétés riemanniennes
BT  - Séminaire Bourbaki : vol. 1979/80, exposés 543-560
AU  - Collectif
T3  - Séminaire Bourbaki
N1  - talk:556
PY  - 1981
SP  - 225
EP  - 245
IS  - 22
PB  - Springer-Verlag
UR  - http://archive.numdam.org/item/SB_1979-1980__22__225_0/
LA  - fr
ID  - SB_1979-1980__22__225_0
ER  - 
%0 Book Section
%A Bérard Bergery, Lionel
%T La courbure scalaire des variétés riemanniennes
%B Séminaire Bourbaki : vol. 1979/80, exposés 543-560
%A Collectif
%S Séminaire Bourbaki
%Z talk:556
%D 1981
%P 225-245
%N 22
%I Springer-Verlag
%U http://archive.numdam.org/item/SB_1979-1980__22__225_0/
%G fr
%F SB_1979-1980__22__225_0
Bérard Bergery, Lionel. La courbure scalaire des variétés riemanniennes, dans Séminaire Bourbaki : vol. 1979/80, exposés 543-560, Séminaire Bourbaki, no. 22 (1981), Exposé no. 556, 21 p. http://archive.numdam.org/item/SB_1979-1980__22__225_0/

[AS] 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. | MR | Zbl

[AU1] T. Aubin - Métriques riemanniennes et courbure, J. Diff. Geom. 4 (1970), 383-424. | MR | Zbl

[AU2] T. Aubin - Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, J. Math. pures et appl. 55 (1976), 269-296. | MR | Zbl

[AU3] T. Aubin - The scalar curvature, in "Differential Geometry and Relativity" (M. Cahen et Flato, Eds), Reidel, Dordrecht (1976), 5-18. | MR | Zbl

[AU4] T. Aubin - Problèmes isopérimétriques et espaces de Sobolev, J. Diff. Geom. 11 (1976), 573-598. | MR | Zbl

[AU5] 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. | MR | Zbl

[AV] A. Avez - Valeur moyenne du scalaire de courbure sur une variété compacte. Applications relativistes. C.R.A.S. 256 (1963), 5271-5273. | MR | Zbl

[BB] L. Bérard Bergery - Sur la courbure des métriques riemanniennes invariantes des groupes de Lie et des espaces homogènes, Annales Sc. Ec. Norm. Sup. Il (1978), 543-576. | Numdam | MR | Zbl

[BE1] M.S. Berger - On the conformal equivalence of compact 2-dimensional manifolds, J. Math. Mech. 19 (1969), 13-18. | MR | Zbl

[BE2] M.S. Berger - Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds, J. Diff. Geom. 5 (1971), 325-332. | MR | Zbl

[BI] E. Bombieri - Régularité des hypersurfaces minimales. Séminaire Bourbaki 21e année 1968/69 - Exposé n° 353 (11 pages). | Numdam | Zbl

[BO1] J.P. Bourguignon - Une stratification de l'espace des structures riemanniennes, Compositio Math., 30(1975), 1-41. | Numdam | MR | Zbl

[BO2] J.P. Bourguignon - Premières formes de Chern des variétés kählériennes compactes. Séminaire Bourbaki 30e année 1977/78 - Exposé n° 507 (18 pages). | Numdam | Zbl

[CA] Première classe de Chern et courbure de Ricci : preuve de la conjecture de Calabi (Séminaire Palaiseau 1978). Astérisque n° 58. | Zbl

[CG] J. Cheeger et D. Gromoll - The splitting theorem for manifolds of non negative Ricci curvature. J. Diff. Geom. 6 (1971), 119-128. | MR | Zbl

[EL] H.I. Eliasson - On variations of metrics, Math. Scand. 29 (1971), 317-327. | MR | Zbl

[FM] A.E. Fischer and J.E. Marsden - Deformations of the scalar curvature, Duke Math. J. 42 (1975), 519-547. | MR | Zbl

[GK] H. Gluck - The generalized Minkowski problem in diffential geometry in the large, Ann. of Math. 96 (1972), 245-275. | MR | Zbl

[GR] 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). | MR | Zbl

[GL1] 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. | MR | Zbl

[GL2] M. Gromov and H.B. Lawson, Jr - The classification of simply connected manifolds of positive scalar curvature (preprint).

[HH] F. Hirzebruch - Topological methods in algebraic topology, Springer Verlag, Berlin Heidelberg New-York, (1966). | MR | Zbl

[HI] N. Hitchin - Harmonic spinors, Adv. in Math. 14 (1974), 1-55. | MR | Zbl

[KW1] 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. | Zbl

[KW2] J.L. Kazdan and F.W. Warner - Curvature functions for 2-manifolds with negative Euler characteristic, Bull. A.M.S. 78 (1972), 570-574. | MR | Zbl

[KW3] 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. | MR | Zbl

[KW4] J.L. Kazdan and F.W. Warner - Curvature functions for 2-manifolds, Proc.of Symposia in Pure Math. 23 (1973), 387-392. | MR | Zbl

[KW5] J.L. Kazdan and F.W. Warner - Curvature functions for compact 2-manifolds, Ann. of Math. 99 (1974), 14-47. | MR | Zbl

[KW6] J.L. Kazdan and F.W. Warner - Curvature functions for open 2-manifolds, Ann. of Math. 99 (1974), 203-219. | MR | Zbl

[KW7] J.L. Kazdan and F.W. Warner - Scalar curvature and conformal deformation of Riemannian structure, J. Diff. Geom. 10 (1975), 113-134. | MR | Zbl

[KW8] 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. | MR | Zbl

[KW9] J.L. Kazdan and F.W. Warner - Prescribing curvatures, Proc. of Symposia in Pure Math. 27 (1975), 309-319. | MR | Zbl

[KW10] 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. | MR | Zbl

[KO] D. Koutroufiotis - On Gaussian curvature and conformal mapping, J. Diff. Geom. 7 (1972), 481-490. | MR | Zbl

[LY] 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. | MR | Zbl

[LE] L. Lemaire - Existence des applications harmoniques et courbure des variétés, Séminaire Bourbaki 32e année 1979/80 Exposé n° 553 (21 pages). | Numdam | Zbl

[LI] A. Lichnerowicz - Spineurs harmoniques, C.R.A.S. 257 A (1963), 7-9. | MR | Zbl

[MI] J. Milnor - Remarks concerning spin manifolds, "Differential geometry and Combinatorial Topology" Princeton University Press (1965), 55-62. | MR | Zbl

[MO1] J. Moser - A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1971), 1077-1092. | MR | Zbl

[MO2] J. Moser - On a nonlinear problem in differential geometry, in Dynamical Systems (M. Peixoto ef.) Academic Press, New York, 1973, 273-280. | MR | Zbl

[ON] B.O.'Neill - The fundamental equations of a submersion, Mich. Math. J. 13 (1966), 459-469. | MR | Zbl

[SY1] 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. | MR | Zbl

[SY2] 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. | MR | Zbl

[SY3] R. Schoen and S.T. Yau - On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), 159-183. | MR | Zbl

[SY4] R. Schoen and S.T. Yau - On the proof of the positive mass conjecture in general relativity, Comm. Math. Phys. 65 (1979), 45-76. | MR | Zbl

[SP] M. Spivak - A comprehensive introduction to differential geometry, Publish or Perish. | Zbl

[TR1] N.S. Trudinger - On imbeddings into Orlicz Spaces and some applications, J. Math. Mech. 17 (1967), 473-483. | MR | Zbl

[TR2] N.S. Trudinger - Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa 22 (1968), 265-274. | Numdam | MR | Zbl

[WW] N.R. Wallach and F.W. Warner - Curvature forms for 2-manifolds, Proc. A.M.S. 25 (1970) 712-713. | MR | Zbl

[YA] H. Yamabe - On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12 (1960), 21-37. | MR | Zbl