Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Annals of the Alexandru Ioan Cuza University - Mathematics

The Journal of "Alexandru Ioan Cuza" University from Iasi

Editor-in-Chief: Oniciuc, Cezar

2 Issues per year


CiteScore 2016: 0.34

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.488

Mathematical Citation Quotient (MCQ) 2015: 0.10

Open Access
Online
ISSN
1221-8421
See all formats and pricing
More options …

Almost Kenmotsu Pseudo-Metric Manifolds

Yaning Wang / Ximin Liu
Published Online: 2014-10-03 | DOI: https://doi.org/10.2478/aicu-2014-0030

Abstract

In this paper, we introduce the geometry of almost Kenmotsu pseudometric manifolds, emphasizing the analogies and differences with respect to the Riemannian case. After giving some fundamental formulas and properties of almost Kenmotsu pseudo-metric manifolds, some classification theorems of such manifolds being locally symmetric or satisfying some nullity conditions are investigated.

Keywords: almost Kenmotsu manifold; pseudo-metric; nullity distribution; locally symmetric; classification theorem.

References

  • 1. Bejancu, A.; Duggal, K.L. - Real hypersurfaces of inde_nite Kaehler manifolds, Internat. J. Math. Math. Sci., 16 (1993), 545-556.CrossrefGoogle Scholar

  • 2. Besse, A.L. - Einstein Manifolds, Ergebnisse der Mathematik und ihrer Grenzgebi- ete (3), 10, Springer-Verlag, Berlin, 1987.Google Scholar

  • 3. Blair, D.E. - Two remarks on contact metric structures, Tôhoku Math. J., 29 (1977), 319-324.Google Scholar

  • 4. Blair, D.E.; Koufogiorgos, T.; Papantoniou, B.J. - Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91 (1995), 189-214.Google Scholar

  • 5. Blair, D.E. - Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203, Birkhäuser Boston, Inc., Boston, MA, 2010.Google Scholar

  • 6. Boeckx, E.; Cho, J.T. - η -parallel contact metric spaces, Differential Geom. Appl., 22 (2005), 275-285.CrossrefGoogle Scholar

  • 7. Calvaruso, G. - Contact Lorentzian manifolds, Differential Geom. Appl., 29 (2011), suppl. 1, S41-S51.Google Scholar

  • 8. Calvaruso, G.; Perrone, D. - Contact pseudo-metric manifolds, Differential Geom. Appl., 28 (2010), 615-634.CrossrefGoogle Scholar

  • 9. De, U.C.; Yildiz, A.; Yaliniz, A.F. - On φ-recurrent Kenmotsu manifolds, Turkish J. Math., 33 (2009), 17-25.Google Scholar

  • 10. Dileo, G. - On the geometry of almost contact metric manifolds of Kenmotsu type, Differential Geom. Appl., 29 (2011), S58-S64.Web of ScienceCrossrefGoogle Scholar

  • 11. Dileo, G. - A classification of certain almost α-Kenmotsu manifolds, Kodai Math. J., 34 (2011), 426-445. Google Scholar

  • 12. Dileo, G.; Pastore, A.M. - Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin, 14 (2007), 343-354.Google Scholar

  • 13. Dileo, G.; Pastore, A.M. - Almost Kenmotsu manifolds with a condition of η - parallelism, Differential Geom. Appl., 27 (2009), 671-679.Web of ScienceCrossrefGoogle Scholar

  • 14. Dileo, G.; Pastore, A.M. - Almost Kenmotsu manifolds and nullity distributions, J. Geom., 93 (2009), 46-61.CrossrefGoogle Scholar

  • 15. Duggal, K.L. - Space time manifolds and contact structures, Internat. J. Math. Math. Sci., 13 (1990), 545-553.CrossrefGoogle Scholar

  • 16. Falcitelli, M.; Pastore, A.M. - Almost Kenmotsu f-manifolds, Balkan J. Geom. Appl., 12 (2007), 32-43.Google Scholar

  • 17. Jun, J.-B.; De, U.C.; Pathak, G. - On Kenmotsu manifolds, J. Korean Math. Soc., 42 (2005), 435-445.Google Scholar

  • 18. Kenmotsu, K. - A class of almost contact Riemannian manifolds, Tôhoku Math. J., 24 (1972), 93-103.Google Scholar

  • 19. Kim, T.W.; Pak, H.K. - Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sin. (Engl. Ser.), 21 (2005), 841-846.CrossrefGoogle Scholar

  • 20. O'Neill, B. - Semi-Riemannian Geometry, With applications to relativity, Pure and Applied Mathematics, 103, Academic Press, Inc., New York, 1983.Google Scholar

  • 21. Pastore, A.M.; Saltarelli, V. - Almost Kenmotsu manifolds with conformal Reeb foliation, Bull. Belg. Math. Soc. Simon Stevin, 18 (2011), 655-666.Google Scholar

  • 22. Sasaki, S.; Hatakeyama, Y. - On differentiable manifolds with certain structures which are closely related to almost contact structure. II, T^ohoku Math. J., 13 (1961), 281-294.Google Scholar

  • 23. Sasaki, S.; Hatakeyama, Y. - On differentiable manifolds with contact metric structures, J. Math. Soc. Japan, 14 (1962), 249-271.CrossrefGoogle Scholar

  • 24. Takahashi, T. - Sasakian manifold with pseudo-Riemannian metric, Tôhoku Math. J., 21 (1969), 271-290. Google Scholar

About the article

Received: 2012-11-20

Revised: 2013-03-28

Accepted: 2013-04-03

Published Online: 2014-10-03


Citation Information: Annals of the Alexandru Ioan Cuza University - Mathematics, ISSN (Online) 1221-8421, DOI: https://doi.org/10.2478/aicu-2014-0030.

Export Citation

© Alexandru Ioan Cuza University in Iaşi . This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in