Skip to main content
SpringerLink
Log in

Almost Cosymplectic and Almost Kenmotsu (κ, μ, ν)-Spaces

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

We study the Riemann curvature tensor of (κ, μ, ν)-spaces when they have almost cosymplectic and almost Kenmotsu structures, giving its writing explicitly. This leads to the definition and study of a natural generalisation of the contact metric (κ, μ, ν)-spaces. We present examples or obstruction results of these spaces in all possible cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alegre P., Blair D. E., Carriazo A.: Generalized Sasakian-space-forms, Israel J. Math. 141, 157–183 (2004)

    MATH  Google Scholar 

  2. Alegre P., Carriazo A.: Structures on generalized Sasakian-space-forms, Differential Geom. Appl. 26((6), 656–666 (2008)

    MathSciNet  MATH  Google Scholar 

  3. Alegre P., Carriazo A.: Submanifolds of generalized Sasakian space forms, Taiwanese J. Math. 13((3), 923–941 (2009)

    MathSciNet  MATH  Google Scholar 

  4. K. Arslan, A. Carriazo, V. Martín-Molina and C. Murathan, The curvature tensor of (κ, μ, ν)-contact metric manifolds, arXiv:1109.625v1

  5. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Second edition. Birkh¨auser, Boston, 2010.

  6. Blair D. E., Koufogiorgos T., Papantoniou B. J.: Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91, 189–214 (1995)

    Google Scholar 

  7. A. Carriazo and V. Martín-Molina, Generalized (κ, μ)-space forms and Dahomothetic deformations, Balkan J. Geom. Appl. 6 (1) (2011), 37–47

    Google Scholar 

  8. A. Carriazo, V. Martín-Molina and M. M. Tripathi, Generalized (κ, μ)-space forms, Mediterr. J. Math. DOI 10.1007/s00009-012-0196-2

  9. P. Dacko, On almost cosymplectic manifolds with the structure vector field ξ belonging to the κ-nullity distribution, Balkan J. Geom. Appl. 5 (no. 2) (2000), 47–60.

    Google Scholar 

  10. Dacko P., Olszak Z.: On almost cosymplectic (κ, μ, ν)-spaces, Banach Center Publ. 69, 211–220 (2005)

    Article  MathSciNet  Google Scholar 

  11. P. Dacko and Z. Olszak, On almost cosymplectic (−1, μ, 0)-spaces, Cent. Eur. J. Math. 3 (no. 2) (2005), 318–330.

  12. H. Endo, On Ricci curvatures of almost cosymplectic manifolds, An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.) 40 (1994), 75–83.

  13. H. Endo, On some properties of almost cosymplectic manifolds, An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.) 42 (1996), 79–94.

  14. H. Endo, On some invariant submanifolds in certain almost cosymplectic manifolds, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 43 (1997), 383–395.

  15. H. Endo, Non-existence of almost cosymplectic manifolds satisfying a certain condition, Tensor (N.S.) 63 (2002), 272–284.

  16. Dileo G., Pastore A. M.: Almost Kenmotsu Manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin 14, 343–354 (2007)

    MATH  Google Scholar 

  17. Dileo G., Pastore A. M.: Almost Kenmotsu Manifolds and Nullity Distributions, J. Geom. 93, 46–61 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. T. W. Kim and H. K. Pak, Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sin. (Engl. Ser.) 21 (2005), 841–846.

    Google Scholar 

  19. T. Koufogiorgos, Contact Riemannian manifolds with constant φ-sectional curvature, Tokyo J. Math. 20 (no. 1) (1997), 55–67.

  20. T. Koufogiorgos, M. Markellos and V. J. Papantoniou, The harmonicity of the Reeb vector fields on contact metric 3-manifolds, Pacific J. Math. 234 (no. 2) (2008), 325–344.

    Google Scholar 

  21. T. Koufogiorgos and C. Tsichlias, On the existence of a new class of contact metric manifolds, Canad. Math. Bull. 43 (no. 4) (2000), 400–447.

    Google Scholar 

  22. Olszak Z.: On almost cosymplectic manifolds, Kodai Math. J. 4, 239–250 (1981)

    MathSciNet  MATH  Google Scholar 

  23. Z. Olszak and R. Rosca, Normal locally conformal almost cosymplectic manifolds, Publ. Math. Debrecen 39 (no. 3-4) (1991), 315–323.

  24. H. Öztürk, N. Aktan and C. Murathan, Almost α-cosymplectic (κ, μ, ν)-spaces, arXiv:1007.0527v1.

Download references

Author information

Authors and Affiliations

  1. Department of Geometry and Topology, Faculty of Mathematics, University of Sevilla, Aptdo. de Correos 1160, 41080, Sevilla, Spain

    Alfonso Carriazo

  2. Centro Universitario de la Defensa, Academia General Militar, Carretera de Huesca, s/n, 50090, Zaragoza, Spain

    Verónica Martín-Molina

Authors
  1. Alfonso Carriazo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Verónica Martín-Molina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alfonso Carriazo.

Additional information

Both authors are partially supported by the MTM2011-22621 grant (MEC, Spain) and by the PAI group FQM-327 (Junta de Andalucía, Spain).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carriazo, A., Martín-Molina, V. Almost Cosymplectic and Almost Kenmotsu (κ, μ, ν)-Spaces. Mediterr. J. Math. 10, 1551–1571 (2013). https://doi.org/10.1007/s00009-013-0246-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00009-013-0246-4

Mathematics Subject Classification (2010)

Keywords

Search

Navigation