Bulletin of the Korean Mathematical Society (대한수학회보)

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

  • Cho, Jong Taek (Department of Mathematics Chonnam National University)
  • Received : 2017.05.31
  • Accepted : 2017.12.29
  • Published : 2018.07.31
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Abstract

In this paper, we give a local and global classification of 3-dimensional H-contact manifolds whose Ricci tensor is ${\eta}$-parallel.

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References

  1. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, second edition, Progress in Mathematics, 203, Birkhauser Boston, Inc., Boston, MA, 2010.
  2. 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.
  3. 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
  4. J. T. Cho and J.-E. Lee, $\eta$-parallel contact 3-manifolds, Bull. Korean Math. Soc. 46 (2009), no. 3, 577-589. https://doi.org/10.4134/BKMS.2009.46.3.577
  5. J. T. Cho and D.-H. Yang, Conformally flat contact three-manifolds, J. Aust. Math. Soc. 103 (2017), no. 2, 177-189. https://doi.org/10.1017/S1446788716000471
  6. T. Koufogiorgos, M. Markellos, and V. J. Papantoniou, The harmonicity of the Reeb vector field on contact metric 3-manifolds, Pacific J. Math. 234 (2008), no. 2, 325-344. https://doi.org/10.2140/pjm.2008.234.325
  7. 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
  8. D. Perrone, Homogeneous contact Riemannian three-manifolds, Illinois J. Math. 42 (1998), no. 2, 243-256.
  9. D. Perrone, Weakly $\phi$-symmetric contact metric spaces, Balkan J. Geom. Appl. 7 (2002), no. 2, 67-77.
  10. D. Perrone, Contact metric manifolds whose characteristic vector field is a harmonic vector field, Differential Geom. Appl. 20 (2004), no. 3, 367-378. https://doi.org/10.1016/j.difgeo.2003.12.007
  11. T. Takahashi, Sasakian $\phi$-symmetric spaces, Tohoku Math. J. (2) 29 (1977), no. 1, 91-113. https://doi.org/10.2748/tmj/1178240699
  12. S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 (1989), no. 1, 349-379. https://doi.org/10.1090/S0002-9947-1989-1000553-9