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Geometry
Volume 2013 (2013), Article ID 654780, 11 pages
http://dx.doi.org/10.1155/2013/654780
Research Article

CR-Submanifolds of Generalized -Space Forms

Department of Mathematics, Jamia Millia Islamia, New Delhi 110025, India

Received 3 January 2013; Revised 28 February 2013; Accepted 3 March 2013

Academic Editor: Michel Planat

Copyright © 2013 Mahmood Jaafari Matehkolaee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Bejancu, “CR submanifolds of a Kaehler manifold. I,” Proceedings of the American Mathematical Society, vol. 69, no. 1, pp. 135–142, 1978. View at Zentralblatt MATH · View at MathSciNet
  2. A. Bejancu, “CR submanifolds of a Kaehler manifold. II,” Transactions of the American Mathematical Society, vol. 250, pp. 333–345, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. M. Kobayashi, “CR submanifolds of a Sasakian manifold,” Tensor, vol. 35, no. 3, pp. 297–307, 1981. View at Zentralblatt MATH · View at MathSciNet
  4. C. Özgür and C. Murathan, “Chen Inequalities for submanifolds of a cosymplectic space form with a semi-symmetric metric connection,” Annals of the Alexandru Ioan Cuza University, no. 2, pp. 395–408, 2012.
  5. M. H. Shahid, “On CR-submanifolds of a certain class of almost contact manifolds,” Rendiconti dell'Istituto di Matematica dell'Università di Trieste, vol. 24, no. 1-2, pp. 147–159, 1992. View at Zentralblatt MATH · View at MathSciNet
  6. M. H. Shahid, “Anti-invariant submanifolds of a Kenmotsu manifold,” Kuwait Journal of Science & Engineering, vol. 23, no. 2, pp. 145–151, 1996. View at Zentralblatt MATH · View at MathSciNet
  7. M. Falcitelli and A. M. Pastore, “Generalized globally framed f-space-forms,” Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, vol. 52, no. 100, pp. 291–305, 2009. View at MathSciNet
  8. K. Yano and M. Kon, CR Submanifolds of Kaehlerian and Sasakian Manifolds, vol. 30, Birkhäuser, Boston, Mass, USA, 1983. View at MathSciNet
  9. K. Yano, “On a structure defined by a tensor field f of type (1,1) satisfying f3+f=0,” Tensor, vol. 14, pp. 99–109, 1963. View at Zentralblatt MATH · View at MathSciNet
  10. D. E. Blair, “Geometry of manifolds with structural group U(n)×O(s),” Journal of Differential Geometry, vol. 4, pp. 155–167, 1970. View at Zentralblatt MATH · View at MathSciNet
  11. K. L. Duggal, S. Ianus, and A. M. Pastore, “Maps interchanging f-structures and their harmonicity,” Acta Applicandae Mathematicae, vol. 67, no. 1, pp. 91–115, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  12. S. I. Goldberg, “On the existence of manifolds with an f-structure,” Tensor, vol. 26, pp. 323–329, 1972. View at MathSciNet
  13. S. I. Goldberg and K. Yano, “Globally framed f-manifolds,” Illinois Journal of Mathematics, vol. 15, pp. 456–474, 1971. View at MathSciNet
  14. D. E. Blair, Contact Manifolds in Riemannian Geometry, vol. 509 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1976. View at MathSciNet
  15. M. Falcitelli and A. M. Pastore, “Almost Kenmotsu f-manifolds,” Balkan Journal of Geometry and Its Applications, vol. 12, no. 1, pp. 32–43, 2007. View at MathSciNet
  16. M. Falcitelli and A. M. Pastore, “f-structures of Kenmotsu type,” Mediterranean Journal of Mathematics, vol. 3, no. 3-4, pp. 549–564, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. P. Alegre, D. E. Blair, and A. Carriazo, “Generalized Sasakian-space-forms,” Israel Journal of Mathematics, vol. 141, pp. 157–183, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. P. Alegre and A. Carriazo, “Structures on generalized Sasakian-space-forms,” Differential Geometry and Its Applications, vol. 26, no. 6, pp. 656–666, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. K. Kenmotsu, “A class of almost contact Riemannian manifolds,” The Tohoku Mathematical Journal II, vol. 24, pp. 93–103, 1972. View at Zentralblatt MATH · View at MathSciNet
  20. D. E. Blair, Riemannian geometry of Contact and Symplectic Manifolds, vol. 203 of Progress in Mathematics, Birkhäuser, Boston, Mass, USA, 2002. View at MathSciNet
  21. M. Kobayashi and S. Tsuchiya, “Invariant submanifolds of an f-manifold with complemented frames,” Kōdai Mathematical Seminar Reports, vol. 24, pp. 430–450, 1972. View at Publisher · View at Google Scholar · View at MathSciNet
  22. J. A. Oubiña, “New classes of almost contact metric structures,” Publicationes Mathematicae Debrecen, vol. 32, no. 3-4, pp. 187–193, 1985. View at Zentralblatt MATH · View at MathSciNet
  23. M. H. Shahid, “CR-submanifolds of a trans-Sasakian manifold I,” Indian Journal of Pure and Applied Mathematics, vol. 22, no. 12, pp. 1007–1012, 1991. View at Zentralblatt MATH · View at MathSciNet
  24. M. H. Shahid, “CR-submanifolds of a trans-Sasakian manifold. II,” Indian Journal of Pure and Applied Mathematics, vol. 25, no. 3, pp. 299–307, 1994. View at Zentralblatt MATH · View at MathSciNet
  25. D. Janssens and L. Vanhecke, “Almost contact structures and curvature tensors,” Kodai Mathematical Journal, vol. 4, no. 1, pp. 1–27, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. A. Carriazo, L. M. Fernández, and A. M. Fuentes, “CR-submanifolds of an S-manifold,” Advances in Geometry, vol. 2, pp. 205–221, 2010.
  27. A. Alghanemi, “CR-submanifolds of an S-manifold,” Turkish Journal of Mathematics, vol. 32, no. 2, pp. 141–154, 2008. View at MathSciNet