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CONFORMALLY FLAT NORMAL ALMOST CONTACT 3-MANIFOLDS
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  • Journal title : Honam Mathematical Journal
  • Volume 38, Issue 1,  2016, pp.59-69
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2016.38.1.59
 Title & Authors
CONFORMALLY FLAT NORMAL ALMOST CONTACT 3-MANIFOLDS
Cho, Jong Taek;
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 Abstract
We classify conformally flat Kenmotsu 3-manifolds and classify conformally flat cosympletic 3-manifolds.
 Keywords
almost contact 3-manifold;conformally flatness;
 Language
English
 Cited by
 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. crossref(new window)

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. crossref(new window)

6.
J.T. Cho, Notes on real hypersurfaces in a complex space form, Bull. Korean Math. Soc. 52(1) (2015), 335-344. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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. crossref(new window)

16.
M. Kimura, Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc. 296 (1986), 137-149. crossref(new window)

17.
S. Montiel, Real hypersurfaces of a complex hyperbolic space, J. Math. Soc. Japan 37 (1985), 515-535. crossref(new window)

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. crossref(new window)

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. crossref(new window)

22.
D. Perrone, Classification of homogeneous almost cosymplectic three-manifolds, Differential. Geom. Appl. 30 (2012), 49-58. crossref(new window)

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. crossref(new window)

26.
S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J. 21 (1969), 21-38. crossref(new window)