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CONFORMALLY FLAT NORMAL ALMOST CONTACT 3-MANIFOLDS

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

Abstract

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

Keywords

almost contact 3-manifold;conformally flatness

Acknowledgement

Supported by : Chonnam National University

References

  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. https://doi.org/10.2140/pjm.2006.226.201
  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. https://doi.org/10.5831/HMJ.2014.36.3.637
  6. J.T. Cho, Notes on real hypersurfaces in a complex space form, Bull. Korean Math. Soc. 52(1) (2015), 335-344. https://doi.org/10.4134/BKMS.2015.52.1.335
  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. https://doi.org/10.1016/j.difgeo.2014.05.002
  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. https://doi.org/10.2748/tmj/1178241594
  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. https://doi.org/10.4134/BKMS.2004.41.4.699
  16. M. Kimura, Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc. 296 (1986), 137-149. https://doi.org/10.1090/S0002-9947-1986-0837803-2
  17. S. Montiel, Real hypersurfaces of a complex hyperbolic space, J. Math. Soc. Japan 37 (1985), 515-535. https://doi.org/10.2969/jmsj/03730515
  18. S. Montiel and A. Romero, On some real hypersurfaces of a complex hyperbolic space, Geom. Dedicata 20 (1986), 245-261. https://doi.org/10.1007/BF00164402
  19. M. Okumura, Some remarks on space with a certain structure, Tohoku Math. J. 14 (1962) 135-145. https://doi.org/10.2748/tmj/1178244168
  20. M. Okumura, Certain almost contact hypersurfaces in Kaehlerian manifolds of constant holomorphic sectional curvature, Tohoku Math. J. (2) 16 (1964), 270-284. https://doi.org/10.2748/tmj/1178243673
  21. M. Okumura, On some real hypersurfaces of a complex projective space, Trans. Amer. Math. Soc. 212 (1975), 355-364. https://doi.org/10.1090/S0002-9947-1975-0377787-X
  22. D. Perrone, Classification of homogeneous almost cosymplectic three-manifolds, Differential. Geom. Appl. 30 (2012), 49-58. https://doi.org/10.1016/j.difgeo.2011.10.003
  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. https://doi.org/10.3792/pja/1195521511
  26. S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J. 21 (1969), 21-38. https://doi.org/10.2748/tmj/1178243031

Cited by

  1. Conformally Flat Almost Kenmotsu 3-Manifolds vol.14, pp.5, 2017, https://doi.org/10.1007/s00009-017-0984-9