Negative scalar curvature metrics on noncompact manifolds
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- by John Bland and Morris Kalka
- Trans. Amer. Math. Soc. 316 (1989), 433-446
- DOI: https://doi.org/10.1090/S0002-9947-1989-0987159-2
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Abstract:
In this paper we prove that every noncompact smooth manifold admits a complete metric of constant negative scalar curvature.References
- Thierry Aubin, Métriques riemanniennes et courbure, J. Differential Geometry 4 (1970), 383–424 (French). MR 279731
- Patricio Aviles and Robert C. McOwen, Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds, J. Differential Geom. 27 (1988), no. 2, 225–239. MR 925121
- Arthur L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987. MR 867684, DOI 10.1007/978-3-540-74311-8
- J. Bland and M. Kalka, Complete metrics of negative scalar curvature on noncompact manifolds, Nonlinear problems in geometry (Mobile, Ala., 1985) Contemp. Math., vol. 51, Amer. Math. Soc., Providence, RI, 1986, pp. 31–35. MR 848930, DOI 10.1090/conm/051/848930
- Zhi Ren Jin, A counterexample to the Yamabe problem for complete noncompact manifolds, Partial differential equations (Tianjin, 1986) Lecture Notes in Math., vol. 1306, Springer, Berlin, 1988, pp. 93–101. MR 1032773, DOI 10.1007/BFb0082927 J. Milnor, Morse theory, Ann. of Math. Studies, no. 51, Princeton Univ. Press, 1963.
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 316 (1989), 433-446
- MSC: Primary 53C20; Secondary 58G30
- DOI: https://doi.org/10.1090/S0002-9947-1989-0987159-2
- MathSciNet review: 987159