CUBO A Mathematical Journal Vol.13, N^o03, (141-152). October 2011

 

On Weak concircular Symmetries of Trans-Sasakian manifolds

 

Shyamal Kumar Hui

Nikhil Banga Sikshan Mahavidyalaya, Bishnupur, Bankura - 722 122, West Bengal, India. email: shyamal_hui@yahoo.co.in

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ABSTRACT

The object of the present paper is to study weakly concircular symmetric and weakly concircular Ricci symmetric trans-Sasakian manifolds.

Keywords. weakly symmetric manifold, weakly concircular symmetric manifold, weakly Ricci symmetric manifold, concircular Ricci tensor, weakly concircular Ricci symmetric manifold, a-Sasakian manifold, p-Kenmotsu manifold, trans-Sasakian manifold.

Mathematics Subject Classification: 53C15, 53C25.

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RESUMEN

El objeto del presente trabajo es el estudio de variedades simetricas debilmente concirculares y variedades simetricas trans-Sasakian debilmente concircular de Ricci.

References

[1] Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509, Springer-Verlag, 1976.         [ Links ]

[2] Blair, D. E. and Oubina, J. A., Conformal and related changes of metric on the product of two almost contact metric manifolds, Publ. Math. Debrecen, 34 (1990), 199-207.         [ Links ]

[3] De, U. C. and Bandyopadhyay, S., On weakly symmetric Riemannian spaces, Publ. Math. Debrecen, 54/3-4 (1999), 377-381.         [ Links ]

[4] De, U. C. and Ghosh, G. C., On weakly concircular Ricci symmetric manifolds, South East Asian J. Math. and Math. Sci., 3(2) (2005), 9-15.         [ Links ]

[5] Oubina, J. A., New class of almost contact metric manifolds, Publ. Math. Debrecen, 32 (1985), 187-193.         [ Links ]

[6] Ozgur, C., On weakly symmetric Kenmotsu manifolds, Diff. Geom.-Dynamical Systems, 8 (2006), 204-209.         [ Links ]

[7] Shaikh, A. A. and Hui, S. K., On weakly concircular symmetric manifolds, Ann. Sti. Ale Univ., "Al. I. CUZA", Din Iasi, LV, f.1 (2009), 167-186.         [ Links ]

[8] Shaikh, A. A. and Hui, S. K., On weak symmetries of trans-Sasakian manifolds, Proc. Estonian Acad. Sci., 58(4) (2009), 213-223.         [ Links ]

[9] Tamassy, L. and Binh, T. Q., On weakly symmetric and weakly projective symmetric Riman-nian manifolds, Coll. Math. Soc., J. Bolyai, 56 (1989), 663-670.         [ Links ]

[10] Tamassy, L. and Binh, T. Q., On weak symmetries of Einstein and Sasakian manifolds, Tensor N. S., 53 (1993), 140-148.         [ Links ]

[11] Yano, K., Concircular geometry I, concircular transformations, Proc. Imp. Acad. Tokyo, 16 (1940), 195-200.         [ Links ]

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Received: April 2010. Revised: September 2010.