Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A REMARK ON QUASI CONTACT METRIC MANIFOLDS

  • Park, JeongHyeong (Department of Mathematics Sungkyunkwan University) ;
  • Sekigawa, Kouei (Department of Mathematics Faculty of Science Niigata University) ;
  • Shin, Wonmin (Department of Mathematics Sungkyunkwan University)
  • Received : 2014.07.03
  • Published : 2015.05.31
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Abstract

As a natural generalization of the contact metric manifolds, Kim, Park and Sekigawa discussed quasi contact metric manifolds based on the geometry of the corresponding quasi $K{\ddot{a}}hler$ cones. In this paper, we show that a quasi contact metric manifold is a contact manifold.

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References

  1. D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Second edition, Progress in Math. 203, Birkhauser, Boston, 2002.
  2. S. Dragomir and D. Perrone, Levi harmonic maps of contact Riemannian manifolds, J. Geom. Anal. 24 (2014), no. 3, 1233-1275. https://doi.org/10.1007/s12220-012-9371-8
  3. A. Gray, Curvature identities for Hermitian and almost Hermitian manifolds, Tohoku Math. J. 28 (1976), no. 4, 601-612. https://doi.org/10.2748/tmj/1178240746
  4. A. Gray and L. Hervella, The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl. 123 (1980), 35-58. https://doi.org/10.1007/BF01796539
  5. J. E. Jin, J. H. Park, and K. Sekigawa, Notes on some classes of 3-dimensional contact metric manifolds, Balkan J. Geom. Appl. 17 (2012), no. 2, 54-65.
  6. J. H. Kim, J. H. Park, and K. Sekigawa, A generalization of contact metric manifolds, Balkan J. Geom. Appl. 19 (2014), no. 2, 94-105.
  7. Z. Olszak, On contact metric manifold, Tohoku Math. J. 31 (1979), no. 2, 247-253. https://doi.org/10.2748/tmj/1178229842
  8. D. Perrone, Remarks on Levi harmonicity of contact semi-Riemannian manifolds, J. Korean Math. Soc. 51 (2014), no. 5, 881-895. https://doi.org/10.4134/JKMS.2014.51.5.881
  9. Y. Tashiro, On contact structure of hypersurfaces in complex manifolds. I, II, Tohoku Math. J. 15 (1963), 62-78; 167-175. https://doi.org/10.2748/tmj/1178243843