Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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NOTES ON ALMOST KENMOTSU THREE-MANIFOLDS

  • Cho, Jong Taek (Department of Mathematics, Chonnam National University)
  • Received : 2014.07.16
  • Accepted : 2014.08.27
  • Published : 2014.09.25
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Abstract

We study 3-dimensional non-unimodular Lie groups with a left-invariant almost Kenmotsu structure.

Keywords

References

  1. D.E. Blair, Riemannian geometry of contact and symplectic manifolds, Second edition, Progr. Math. 203, Birkhauser Boston, Inc., Boston, MA, 2010.
  2. D.E. Blair and H. Chen, A classification of 3-dimensional contact metric manifolds with $Q{\varphi}={\varphi}Q$, II, Bull. Inst. Math. Acad. Sinica, 20(4) (1992), 379-384.
  3. J.T. Cho, Contact 3-manifolds with the Reeb flow symmetry, Tohoku Math. J., to appear.
  4. J.T. Cho, Reeb flow symmetry on almost cosymplectic three-manifolds, preprint.
  5. J.T. Cho and M. Kimura, Reeb flow symmetry on almost contact three-manifolds, Diff. Geom. Appl. (2014), http://dx.doi.org/10.1016/j.difgeo.2014.05.002.
  6. J.T. Cho, Local symmetry on almost Kenmotsu three-manifolds, preprint.
  7. G. Dileo and A.M. Pastore, Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin, 14 (2007), 343-354.
  8. G. Dileo and A.M. Pastore, Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93 (2009), 46-61. https://doi.org/10.1007/s00022-009-1974-2
  9. J. Inoguchi, Pseudo-symmetric Lie groups of dimension 3, Bull. Fac. Edu. Utsunomiya Univ. Sect. 2, 57 (2007), 1-5.
  10. J. Inoguchi, Minimal surfaces in 3-dimensional solvable Lie groups, Chinese Ann. Math. B. 24 (2003), 73-84. https://doi.org/10.1142/S0252959903000086
  11. J. Inoguchi and Ji-Eun Lee, Slant curves in 3-dimensional almost contact metric geometry, preprint.
  12. K. Kenmotsu, A class of contact Riemannian Manifolds, Tohoku Math. J. 24 (1972), 93-103. https://doi.org/10.2748/tmj/1178241594
  13. T.W. Kim and H.K. Pak, Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sinica, 21 (2005), 841-846. https://doi.org/10.1007/s10114-004-0520-2
  14. J. Milnor, Curvature of left invariant metrics on Lie groups, Adv. in Math. 21 (1976), 293-329. https://doi.org/10.1016/S0001-8708(76)80002-3

Cited by

  1. Conformally Flat Almost Kenmotsu 3-Manifolds vol.14, pp.5, 2017, https://doi.org/10.1007/s00009-017-0984-9
  2. CONFORMALLY FLAT NORMAL ALMOST CONTACT 3-MANIFOLDS vol.38, pp.1, 2016, https://doi.org/10.5831/HMJ.2016.38.1.59