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`GeometryVolume 2013 (2013), Article ID 654780, 11 pageshttp://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

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.

1. A. Bejancu, “CR submanifolds of a Kaehler manifold. I,” Proceedings of the American Mathematical Society, vol. 69, no. 1, pp. 135–142, 1978.
2. A. Bejancu, “CR submanifolds of a Kaehler manifold. II,” Transactions of the American Mathematical Society, vol. 250, pp. 333–345, 1979.
3. M. Kobayashi, “CR submanifolds of a Sasakian manifold,” Tensor, vol. 35, no. 3, pp. 297–307, 1981.
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.
6. M. H. Shahid, “Anti-invariant submanifolds of a Kenmotsu manifold,” Kuwait Journal of Science & Engineering, vol. 23, no. 2, pp. 145–151, 1996.
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.
8. K. Yano and M. Kon, CR Submanifolds of Kaehlerian and Sasakian Manifolds, vol. 30, Birkhäuser, Boston, Mass, USA, 1983.
9. K. Yano, “On a structure defined by a tensor field f of type $\left(1,1\right)$ satisfying ${f}^{3}+f\text{}=0$,” Tensor, vol. 14, pp. 99–109, 1963.
10. D. E. Blair, “Geometry of manifolds with structural group $U\left(n\right)×O\left(s\right)$,” Journal of Differential Geometry, vol. 4, pp. 155–167, 1970.
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.
12. S. I. Goldberg, “On the existence of manifolds with an f-structure,” Tensor, vol. 26, pp. 323–329, 1972.
13. S. I. Goldberg and K. Yano, “Globally framed f-manifolds,” Illinois Journal of Mathematics, vol. 15, pp. 456–474, 1971.
14. D. E. Blair, Contact Manifolds in Riemannian Geometry, vol. 509 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1976.
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.
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.
17. P. Alegre, D. E. Blair, and A. Carriazo, “Generalized Sasakian-space-forms,” Israel Journal of Mathematics, vol. 141, pp. 157–183, 2004.
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.
19. K. Kenmotsu, “A class of almost contact Riemannian manifolds,” The Tohoku Mathematical Journal II, vol. 24, pp. 93–103, 1972.
20. D. E. Blair, Riemannian geometry of Contact and Symplectic Manifolds, vol. 203 of Progress in Mathematics, Birkhäuser, Boston, Mass, USA, 2002.
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.
22. J. A. Oubiña, “New classes of almost contact metric structures,” Publicationes Mathematicae Debrecen, vol. 32, no. 3-4, pp. 187–193, 1985.
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.
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.
25. D. Janssens and L. Vanhecke, “Almost contact structures and curvature tensors,” Kodai Mathematical Journal, vol. 4, no. 1, pp. 1–27, 1981.
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.