Beyond Generalized Sasakian-Space-Forms!

  • Alfonso Carriazo
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


In this paper we will review some recent advances on the theory of generalized Sasakian-space-forms, as well as some new directions in which this theory is being developed now.


Vector Field Curvature Tensor Warped Product Sasakian Manifold Riemann Curvature Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author is partially supported by MTM2011-22621 grant (MINECO, Spain) and by the PAIDI group FQM-327 (Junta de Andalucía, Spain). He wants to express his deepest gratitude to Prof. Young Jin Suh for his kind invitation to participate in this Conference.


  1. 1.
    Alegre, P., Blair, D.E., Carriazo, A.: Generalized Sasakian-space-forms. Israel J. Math. 141, 157–183 (2004)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Alegre, P., Carriazo, A.: Structures on generalized Sasakian-space-forms. Differ. Geom. Appl. 26, 656–666 (2008)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Alegre, P., Carriazo, A.: Generalized Sasakian space forms and conformal changes of the metric. Results Math. 59, 485–493 (2011)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Alegre, P., Carriazo, A.: Semi-Riemannian generalized Sasakian-space-forms. SubmittedGoogle Scholar
  5. 5.
    Arslan, K., Carriazo, A., Martín-Molina, V., Murathan, C.: The curvature tensor of (κ, μ, ν)-contact metric manifolds. SubmittedGoogle Scholar
  6. 6.
    Blair, D.E.: Riemannian Geometry of Contact and Symplectic Manifolds. Birkhäuser, Boston (2002)CrossRefMATHGoogle Scholar
  7. 7.
    Blair, D.E., Koufogiorgos, T., Papantoniou, B.J.: Contact metric manifolds satisfying a nullity condition. Israel J. Math. 91, 189–214 (1995)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Bueken, P., Vanhecke, L.: Curvature characterizations in contact geometry. Riv. Mat. Univ. Parma 14(4), 303–313 (1988)MATHMathSciNetGoogle Scholar
  9. 9.
    Calvaruso, G., Perrone, D.: Contact pseudo-metric manifolds. Differ. Geom. Appl 28, 615–634 (2010)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Carriazo, A.: On generalized Sasakian-space-forms. In: Suh, Y.J., Montiel, S., Pak, J.S., Choi, Y.S. (eds.) Proceedings of the Ninth International Workshop on Diff. Geom., pp. 31–39. Kyungpook National University, Taegu (2005)Google Scholar
  11. 11.
    Carriazo, A., Fernández, L.M., Fuentes, A.M.: Generalized S-space-forms with two structure vector fields. Adv. Geom. 10, 205–219 (2010)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Carriazo, A., Martín-Molina, V.: Generalized (κ, μ)-space forms and D a-homothetic deformations. Balkan J. Geom. Appl. 6, 37–47 (2011)Google Scholar
  13. 13.
    Carriazo, A., Martín-Molina, V.: Almost cosymplectic and almost Kenmotsu (κ, μ, ν)-spaces. Mediterr. J. Math. 10, 1551–1571 (2013)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Carriazo, A., Martín-Molina, V., Tripathi, M.M.: Generalized (κ, μ)-space forms. Mediterr. J. Math. 10, 475–496 (2013)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Chern, S.-S.: What is Geometry? Am. Math. Monthly 97, 679–686 (1990)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Duggal, K.L.: Space time manifolds and contact structures. Int. J. Math. Math. Sci. 16, 545–553 (1990)CrossRefGoogle Scholar
  17. 17.
    Falcitelli, M., Pastore, A.M.: Generalized globally framed f-space-forms. Bull. Math. Soc. Sci. Math. Roumanie 52, 291–305 (2009)MathSciNetGoogle Scholar
  18. 18.
    Fernández, L.M., Fuentes, A.M., Prieto-Martín, A.: Generalized S-space-forms. Publ. Inst. Math. 94, 151–161 (2013)CrossRefGoogle Scholar
  19. 19.
    Koufogiorgos, T.: Contact Riemannian manifolds with constant ϕ-sectional curvature. Tokyo J. Math. 20, 55–67 (1997)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Koufogiorgos, T., Markellos, M., Papantoniou, V. J.: The harmonicity of the Reeb vector fields on contact metric 3-manifolds. Pac. J. Math. 234, 325–344 (2008)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Lee, J.W.: Constancy of ϕ-holomorphic sectional curvature for an indefinite generalized g.f.f.-space form. Adv. Math. Phys. (2011)Google Scholar
  22. 22.
    Marrero, J.C.: The local structure of trans-Sasakian manifolds. Ann. Mat. Pura Appl. 162, 77–86 (1992)CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Oubiña, J.A.: New classes of almost contact metric structures. Publ. Math. Debrecen 32, 187–193 (1985)MATHMathSciNetGoogle Scholar
  24. 24.
    Tripathi, M.M., Kilic, E., Perktas, S.Y., Keles, S.: Indefinite almost paracontact metric manifolds. Int. J. Math. Math. Sci., 1687–1705 (2010)Google Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of Geometry and Topology, Faculty of MathematicsUniversity of SevilleSevilleSpain

Personalised recommendations