• Cho, Jong Taek (Department of Mathematics, Chonnam National University)
  • Received : 2015.09.24
  • Accepted : 2016.01.25
  • Published : 2016.03.25


We classify conformally flat Kenmotsu 3-manifolds and classify conformally flat cosympletic 3-manifolds.


Supported by : Chonnam National University


  1. J. Berndt, Real hypersurfaces with constant principal curvatures in complex hyperbolic space J. Reine Angew. Math. 395 (1989), 132-141.
  2. D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Second edition, Progr. Math. 203, Birkhauser Boston, Inc., Boston, MA, 2010.
  3. M. Brozos-Vazquez, E. Garcia-Rio and R. Vazquez-Lorenzo, Complete locally conformally flat manifolds of negative curvature, Pacific J. Math. 226 (2006), 201-219.
  4. T. E. Cecil and P. J. Ryan, Focal sets and real hypersurfaces in complex projective space, Trans. Amer. Math. Soc. 269 (1982), 481-499.
  5. J.T. Cho, Notes on almost Kenmotsu three-manifolds, Honam Math. J. 36(3) (2014), 637-645.
  6. J.T. Cho, Notes on real hypersurfaces in a complex space form, Bull. Korean Math. Soc. 52(1) (2015), 335-344.
  7. J.T. Cho, Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J., to appear.
  8. J.T. Cho, Reeb flow symmetry on almost coymplectic three-manifolds, submitted.
  9. J.T. Cho and M. Kimura, Reeb flow symmetry on almost contact three-manifolds, Differential Geom. Appl. 35 (2014), 266-273.
  10. J.T. Cho and D-h. Yang, Conformally flat contact 3-manifolds, submitted.
  11. P. Dacko and Z. Olszak, On conformally flat almost cosymplectic manifolds with Kaherian manifolds, Ren. Sem. Math. Univ. Pol. Torino 56(1) (1998), 89-103.
  12. J. Inoguchi, A note on almost contact Riemannian 3-manifolds II, preprint.
  13. K. Kenmotsu, A class of contact Riemannian Manifolds, Tohoku Math. J. 24 (1972), 93-103.
  14. U-H. Ki, H. Nakagawa and Y.J. Suh, Real hypersurfaces with harmonic Weyl tensor of a complex space form, Hiroshima Math. J. 20 (1990), 93-102.
  15. U.K. Kim, Nonexistence of Ricci-parallel real hypersurfaces in $P_2{\mathbb{C}}$ or $H_2{\mathbb{C}}$, Bull. Korean Math. Soc. 41 (2004), 699-708.
  16. M. Kimura, Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc. 296 (1986), 137-149.
  17. S. Montiel, Real hypersurfaces of a complex hyperbolic space, J. Math. Soc. Japan 37 (1985), 515-535.
  18. S. Montiel and A. Romero, On some real hypersurfaces of a complex hyperbolic space, Geom. Dedicata 20 (1986), 245-261.
  19. M. Okumura, Some remarks on space with a certain structure, Tohoku Math. J. 14 (1962) 135-145.
  20. M. Okumura, Certain almost contact hypersurfaces in Kaehlerian manifolds of constant holomorphic sectional curvature, Tohoku Math. J. (2) 16 (1964), 270-284.
  21. M. Okumura, On some real hypersurfaces of a complex projective space, Trans. Amer. Math. Soc. 212 (1975), 355-364.
  22. D. Perrone, Classification of homogeneous almost cosymplectic three-manifolds, Differential. Geom. Appl. 30 (2012), 49-58.
  23. R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math. 19 (1973), 495-506.
  24. R. Takagi, Real hypersurfaces in a complex projective space with constant principal curvatures I, J. Math. Soc. Japan 15 (1975), 43-53.
  25. S. Tanno, Locally symmetric K-contact Riemannian manifolds, Proc. Japan Acad. 43 (1967), 581-583.
  26. S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J. 21 (1969), 21-38.

Cited by

  1. Conformally Flat Almost Kenmotsu 3-Manifolds vol.14, pp.5, 2017,