Tohoku Mathematical Journal

Torsion and deformation of contact metric structures on $3$-manifolds

Samuel I. Goldberg and Gábor Tóth

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Tohoku Math. J. (2), Volume 39, Number 3 (1987), 365-372.

First available in Project Euclid: 3 May 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]


Goldberg, Samuel I.; Tóth, Gábor. Torsion and deformation of contact metric structures on $3$-manifolds. Tohoku Math. J. (2) 39 (1987), no. 3, 365--372. doi:10.2748/tmj/1178228283.

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  • [1] M. BERGER AND D. EBIN, Some decompositions of thespace of symmetric tensors on a Riemannian manifold, J. Diff. Geom. 3 (1969), 379-392.
  • [2] D. E. BLAIR, Contact manifolds in Riemannian Geometry, Lecture Notes in Math., 509, Springer-Verlag, Berlin and New York, 1976.
  • [3] S. S. CHERN AND R. S. HAMILTON, On Riemannian metrics adapted to three-dimensiona contact manifolds, Lecture Notes in Math., Springer-Verlag, Berlin and New York, Vol. 1111, 1985, 279-308.
  • [4] S. I. GOLDBERG, Nonnegatively curved contact manifolds, Proc. Amer. Math. Soc. 9 (1986), 651-656.
  • [5] R. S. HAMILTON, Three-manifolds with positive Ricci curvature, J. Diff. Geom. 17 (1982), 255-306.
  • [6] J. MARTINET, Formes de contact sur les varietes de dimension 3, Proc. Liverpool Singu larities Sympos. II, Springer Lecture Notes in Math. 209 (1971), 142-163.
  • [7] H. SATO, Remarks concerning contact manifolds, Tohoku Math. J. 29 (1977), 577-584

See also

  • Part I: Samuel I. Goldberg, Gábor Tóth. Addendum to: ``Torsion and deformation of contact metric structures on $3$-manifolds''. Tohoku Math. J., Volume 41, Number 2 (1989), pp. 259-262.