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Curvature of contact Riemannian three-manifolds with critical metrics

Part of the Lecture Notes in Mathematics book series (LNM,volume 1410)

Keywords

  • Constant Curvature
  • Contact Structure
  • Contact Manifold
  • Bisectional Curvature
  • Positive Sectional Curvature

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References

  1. D. E. Blair, Critical associated metrics on contact manifolds, J. Austral. Math. Soc. (Series A) 37(1984), 82–88.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. —, On the non-regularity of tangent sphere bundles, Proc. Royal Soc. of Edinburgh, 82A(1978), 13–17.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Y. Carrière, Flots riemanniens, Astérisque, 116(1984), 31–52.

    MathSciNet  MATH  Google Scholar 

  4. S. S. Chern and R. S. Hamilton, On Riemannian metrics adapted to three-dimensional contact manifolds, Lecture Notes in Math., 1111, Springer-Verlag, Berlin and New York, 1985, 279–308.

    MATH  Google Scholar 

  5. S. I. Goldberg, Nonnegatively curved contact manifolds, Proc. Amer. Math. Soc. 96(1986), 651–656.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. S. I. Goldberg and G. Toth, Torsion and deformation of contact metric structures on 3-manifolds, Tohoku Math. J. 39(1987), 365–372.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17(1982), 255–306.

    MathSciNet  MATH  Google Scholar 

  8. J. Martinet, Formes de contact sur les variétés de dimension 3, Proc. Liverpool Singularities Sympos. II, Lecture Notes in Math. 209, Springer-Verlag, Berlin and New York, 1971, 142–163.

    CrossRef  Google Scholar 

  9. G. Monna, Techniques de h-platitude en géométrie de contact, Thesis, U.S.T.L., Montpellier, 1981.

    Google Scholar 

  10. F. Raymond, Classification of the actions of the circle on 3-manifolds, Trans. Amer. Math. Soc. 131(1968), 51–78.

    MathSciNet  MATH  Google Scholar 

  11. Y. T. Siu and S. T. Yau, Compact Kaehler manifolds of positive bisectional curvature, Invent. Math. 59(1980), 189–204.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. S. Tanno, Variational problems on contact Riemannian manifolds, preprint.

    Google Scholar 

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© 1989 Springer-Verlag

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Goldberg, S.I., Perrone, D., Toth, G. (1989). Curvature of contact Riemannian three-manifolds with critical metrics. In: Carreras, F.J., Gil-Medrano, O., Naveira, A.M. (eds) Differential Geometry. Lecture Notes in Mathematics, vol 1410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086424

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  • DOI: https://doi.org/10.1007/BFb0086424

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  • Print ISBN: 978-3-540-51885-3

  • Online ISBN: 978-3-540-46858-5

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