APM  Vol.2 No.3 , May 2012
On Lorentzian α-Sasakian Manifolds
ABSTRACT
The object of the present paper is to study Lorentzian α-Sasakian manifolds satisfying certain conditions on the W2- curvature tensor.

Cite this paper
S. Lokesh, V. Bagewadi and K. Kumar, "On Lorentzian α-Sasakian Manifolds," Advances in Pure Mathematics, Vol. 2 No. 3, 2012, pp. 177-182. doi: 10.4236/apm.2012.23024.
References
[1]   G. P. Pokhariyal and R. S. Mishra, “The Curvature Tensor and Their Relativistic Significance,” Yokohoma Mathematical Journal, Vol. 18, 1970, pp. 105-108.

[2]   G. P. Pokhariyal, “Study of a New Curvature Tensor in a Sasakian Manifold,” Tensor N.S., Vol. 36, No. 2, 1982, pp. 222-225.

[3]   K. Matsumoto, S. Ianus and I. Mihai, “On P-Sasakian manifolds Which Admit Certain Tensor Fields,” Publicationes Mathematicae Debrecen, Vol. 33, 1986, pp. 61-65.

[4]   A, Yildiz and U. C. De, “On a Type of Kenmotsu Manifolds,” Differential Geometry-Dynamical Systems, Vol. 12, 2010, pp. 289-298.

[5]   Venkatesha, C. S. Bagewadi and K. T. Pradeep Kumar, “Some Results on Lorentzian Para-Sasakian Manifolds,” ISRN Geometry, Vol. 2011, Article ID 161523.

[6]   S. Tanno, “The Automorphism Groups of Almost Contact Riemannian Manifolds,” Tohoku Mathematical Journal, Vol. 21, No. 1, 1969, pp. 21-38. doi:10.2748/tmj/1178243031

[7]   A. Gray and L. M. Hervella, “The Sixteen Classes of almost Hermitian Manifolds and Their Linear Invariants,” Annali di Matematica Pura ed Applicata, Vol. 123, No. 4, 1980, pp. 35-58. doi:10.1007/BF01796539

[8]   S. Dragomir and L. Ornea, “Locally Conformal Kaehler Geometry, Progress in Mathematics,” Birkhauser Boston, Inc., Boston, 1998.

[9]   J. A. Oubina, “New Classes of Contact Metric Structures,” Publicationes Mathematicae Debrecen, Vol. 32, No. 4, 1985, pp. 187-193.

[10]   J. C. Marrero, “The Local Structure of Trans-Sasakian Manifolds,” Annali di Matematica Pura ed Applicata, Vol. 162, No. 4, 1992, pp. 77-86. doi:10.1007/BF01760000

[11]   J. C. Marrero and D. Chinea, “On Trans-Sasakian Manifolds,” Proceedings of the XIVth Spanish-Portuguese Conference on Mathematics, University La Laguna, Vol. I-III, 1990, pp. 655-659.

[12]   D. E. Blair, “Contact Manifolds in Riemannian Geometry,” Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1976.

[13]   K. Kenmotsu, “A Class of Almost Contact Riemannian Manifolds,” Tohoku Mathematical Journal, Vol. 24, No. 1, 1972, pp. 93-103. doi:10.2748/tmj/1178241594

[14]   M. M. Tripathi, “Trans-Sasakian Manifolds Are Generalized Quasi-Sasakian,” Nepali Mathematical Sciences Report, Vol. 18, No. 2, 2000, pp. 11-14.

[15]   D. E. Blair and J. A. Oubina, “Conformal and Related Changes of Metric on the Product of Two Almost Contact Metric Manifolds,” Publications Matematiques, Vol. 34, 1990, pp. 99-207.

[16]   D. Janssens and L. Vanhecke, “Almost Contact Structures and Curvature Tensors,” Kodai Mathematical Journal, Vol. 4, No. 1, 1981, pp. 1-27. doi:10.2996/kmj/1138036310

[17]   A. Yildiz and C. Murathan, “On Lorentizian _α-Sasakian Manifolds,” Kyungpook Mathematical Journal, Vol. 45, No. 1, 2005, pp. 95-103.

[18]   U. C. De and M. M. Tripathi, “Ricci Tensor in 3-Dimen- sional Trans-Sasakian Manifolds,” Kyungpook Mathematical Journal, Vol. 43, 2003, pp. 247-255.

[19]   K. Matsumoto and I. Mihai, “On a Certain Transformation in a Lorentzian Para-Sasakian Manifold,” Tensor N.S., Vol. 47, 1988, pp. 189-197.

[20]   K. Yano and M. Kon, “Structures on Manifolds,” Series in Pure Mathematics, Vol. 3, World Scientific Publishing Co., Singapore, 1984.

[21]   G. P. Pokhariyal and R. S. Mishra, “Curvature Tensor and Their Relativistic Significance II,” Yokohama Mathematical Journal, Vol. 19, 1971, pp. 97-103.

 
 
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