Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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η-PARALLEL CONTACT 3-MANIFOLDS

  • Cho, Jong-Taek (DEPARTMENT OF MATHEMATICS CHONNAM NATIONAL UNIVERSITY) ;
  • Lee, Ji-Eun (NATIONAL INSTITUTE FOR MATHEMATICAL SCIENCES)
  • Published : 2009.05.31
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Abstract

In this paper, we give a classification of contact 3-manifolds whose Ricci tensors are $\eta$-parallel.

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References

  1. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203. Birkhauser Boston, Inc., Boston, 2002
  2. D. E. Blair, Critical associated metrics on contact manifolds, J. Austral. Math. Soc. Ser. A 37 (1984), no. 1, 82–88 https://doi.org/10.1017/S1446788700021753
  3. D. E. Blair, When is the tangent sphere bundle locally symmetric?, Geometry and topology, 15–30, World Sci. Publishing, Singapore, 1989
  4. D. E. Blair, T. Koufogiorgos, and R. Sharma, A classification of 3-dimensional contact metric manifolds with Q$\phi = \phi$Q, Kodai Math. J. 13 (1990), no. 3, 391–401 https://doi.org/10.2996/kmj/1138039284
  5. D. E. Blair and R. Sharma, Three-dimensional locally symmetric contact metric manifolds, Boll. Un. Mat. Ital. A (7) 4 (1990), no. 3, 385–390
  6. D. E. Blair and L. Vanhecke, Symmetries and A-symmetric spaces, Tohoku Math. J. (2) 39 (1987), no. 3, 373–383
  7. E. Boeckx and J. T. Cho, Locally symmetric contact metric manifolds, Monatsh. Math. 148 (2006), no. 4, 269–281 https://doi.org/10.1007/s00605-005-0366-4
  8. E. Boeckx, P. Bueken, and L. Vanhecke, A-symmetric contact metric spaces, Glasg. Math. J. 41 (1999), no. 3, 409–416
  9. G. Calvaruso, D. Perrone, and L. Vanhecke, Homogeneity on three-dimensional contact metric manifolds, Israel J. Math. 114 (1999), 301–321 https://doi.org/10.1007/BF02785585
  10. S. S. Chern and R. S. Hamilton, On Riemannian metrics adapted to three-dimensional contact manifolds, With an appendix by Alan Weinstein. Lecture Notes in Math., 1111, Workshop Bonn 1984 (Bonn, 1984), 279–308, Springer, Berlin, 1985 https://doi.org/10.1007/BFb0084596
  11. F. Gouli-Andreou and P. J. Xenos, On 3-dimensional contact metric manifolds with $\nabla_{\varepsilon \tau}$= 0, J. Geom. 62 (1998), no. 1-2, 154–165 https://doi.org/10.1007/BF01237607
  12. J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293–329 https://doi.org/10.1016/S0001-8708(76)80002-3
  13. D. Perrone, Torsion and critical metrics on contact three-manifolds, Kodai Math. J. 13 (1990), no. 1, 88–100 https://doi.org/10.2996/kmj/1138039163
  14. D. Perrone, Weakly $\phi$-symmetric contact metric spaces, Balkan J. Geom. Appl. 7 (2002), no. 2, 67–77
  15. T. Takahashi, Sasakian $\phi$-symmetric spaces, Tohoku Math. J. (2) 29 (1977), no. 1, 91–113
  16. S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 (1989), no. 1, 349–379