Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

QUASI CONTACT METRIC MANIFOLDS WITH KILLING CHARACTERISTIC VECTOR FIELDS

  • Received : 2019.11.04
  • Accepted : 2020.05.07
  • Published : 2020.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

An almost contact metric manifold is called a quasi contact metric manifold if the corresponding almost Hermitian cone is a quasi Kähler manifold, which was introduced by Y. Tashiro [9] as a contact O*-manifold. In this paper, we show that a quasi contact metric manifold with Killing characteristic vector field is a K-contact manifold. This provides an extension of the definition of K-contact manifold.

Keywords

References

  1. D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, 203, Birkhauser Boston, Inc., Boston, MA, 2002. https://doi.org/10.1007/978-1-4757-3604-5
  2. Y. D. Chai, J. H. Kim, J. H. Park, K. Sekigawa, and W. M. Shin, Notes on quasi contact metric manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 62 (2016), no. 2, vol. 1, 349-359.
  3. S. H. Chun, J. H. Park, and K. Sekigawa, Notes on minimal unit Killing vector fields, Bull. Korean Math. Soc. 55 (2018), no. 5, 1339-1350. https://doi.org/10.4134/BKMS.b170760
  4. A. Gray and L. M. Hervella, The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl. (4) 123 (1980), 35-58. https://doi.org/10.1007/BF01796539
  5. 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.
  6. F. Malek and R. Hojati, Quasi contact metric manifolds with constant sectional curva- ture, Tokyo J. Math. 41 (2018), no. 2, 515-525. https://projecteuclid.org/euclid.tjm/1516935626 https://doi.org/10.3836/tjm/1502179276
  7. J. H. Park, K. Sekigawa, and W. Shin, A remark on quasi contact metric manifolds, Bull. Korean Math. Soc. 52 (2015), no. 3, 1027-1034. https://doi.org/10.4134/BKMS.2015.52.3.1027
  8. S. Tanno, Locally symmetric K-contact Riemannian manifolds, Proc. Japan Acad. 43 (1967), 581-583. http://projecteuclid.org/euclid.pja/1195521511 https://doi.org/10.3792/pja/1195521511
  9. Y. Tashiro, On contact structure of hypersurfaces in complex manifolds. II, Tohoku Math. J. (2) 15 (1963), 167-175. https://doi.org/10.2748/tmj/1178243843
  10. G. Thompson, Normal forms for skew-symmetric matrices and Hamiltonian systems with first integrals linear in momenta, Proc. Amer. Math. Soc. 104 (1988), no. 3, 910-916. https://doi.org/10.2307/2046815