# NOTES ON ALMOST KENMOTSU THREE-MANIFOLDS

• Received : 2014.07.16
• Accepted : 2014.08.27
• Published : 2014.09.25
• 50 4

#### Abstract

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

#### Keywords

almost Kenmotsu 3-manifold;non-unimodular Lie group;conformally flat

#### 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. https://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. K. Kenmotsu, A class of contact Riemannian Manifolds, Tohoku Math. J. 24 (1972), 93-103. https://doi.org/10.2748/tmj/1178241594
10. J. Inoguchi, Pseudo-symmetric Lie groups of dimension 3, Bull. Fac. Edu. Utsunomiya Univ. Sect. 2, 57 (2007), 1-5.
11. J. Inoguchi, Minimal surfaces in 3-dimensional solvable Lie groups, Chinese Ann. Math. B. 24 (2003), 73-84. https://doi.org/10.1142/S0252959903000086
12. J. Inoguchi and Ji-Eun Lee, Slant curves in 3-dimensional almost contact metric geometry, preprint.
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