On Weak Symmetries of Generalized Sasakian-Space-Forms

Authors

  • D.G. Prakasha Department of Mathematics, Karnatak University, Dharwad
  • Vasant Chavan Department of Mathematics, Karnatak University, Dharwad

DOI:

https://doi.org/10.26713/cma.v5i3.249

Keywords:

Generalized Sasakian-space-forms, Weakly symmetric, Weakly Riccisymmetric, Specially weakly Ricci-symmetric

Abstract

The purpose of the paper is to study weakly symmetric and weakly Ricci-symmetric generalized Sasakian-space-forms. We consider the locally symmetric and recurrent type of weakly symmetric generalized Sasakian-space-forms. Also, locally Ricci-symmetric and Riccirecurrent weakly Ricci-symmetric generalized Sasakian-space-forms are discussed.

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References

P. Alegre, D.E. Blair and A. Carriazo, Generalized Sasakian-space-forms, Israel J. Math. 14 (2004), 157-183.

P. Alegre and A. Carriazo, Structure on generalized Sasakian-space-forms, Differential Geom. Appl. 26 (2008), 656-666.

P. Alegre and A. Carriazo, Submanifolds of generalized Sasakian-space-forms, Taiwanese J. Math. 13 (2009), 923-941.

P. Alegre and A. Carriazo, Generalized Sasakian-space-forms and conformal change of metric, Results Math. 59 (2011), 485-493.

D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol. 509. Springer-Verlag, Berlin,New-York, 1976.

U. C. De and A. Sarkar, On the projective curvature tensor of generalized Sasakian space-forms, Quaestiones Mathematicae, 33 (2010), 245-252.

U. C. De and S. Bandyopadhyay, On weakly symmetric spaces, Publ. Math. Debrecen 54 (1999), 377-381.

U. C. De, A. A Shaikh and S. Biswas, On weakly symmetric contact metric manifolds, Tensor (N.S) 64 (2) (2003), 170-175.

S. K. Hui and A. Sarkar, On the W2-curvature tensor of generalized Sasakian-spaceforms, Math. Pannonica,

U. K. Kim, Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms, Note di Matematica 26 (2006), 55-67.

C. Ozgur, On weakly symmetric Kenmotsu manifolds, Diff. Geom.-Dyn. Syst. 8(2006), 204-209.

D. G. Prakasha, On generalized Sasakian-space-forms with Weyl-conformal curvature tensor, Lobachevskii J. Math. 33(3) (2012), 223-228.

D. G. Prakasha, S. K. Hui, and K. Vikas, On weakly $phi$-Ricci symmetric Kenmotsu manifolds, Int. J. Pure. Appl. Math. 95(4) (2014), 515-521.

D. G. Prakasha and H. G. Nagaraja, On quasi-conformally flat and quasi-conformally semisymmetric generalized Sasakian-space-forms, Cubo (Temuco) 15(3) (2013), 59-70.

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

A. Shaikh and S. K. Jana, On weakly symmetric Riemannian manifolds, Publ. Math. Debrecen. 71 (2007), 27-41.

H. Singh and Q. Khan, On special weakly symmetric Riemannian Manifolds, Publ. Math.,

Debrecen 3 (2001), 523-536.

L. Tamassy and T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Colloq. Math. Soc. J. Bolyai. 56 (1992), 663-670.

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

S. Yadav and D. L. Suthar, Some global properties of $(f_1,f_2,f_3)_{2n+1}$-manifolds, Acta

Univ. Apulensis. 33 (2013), 247-256.

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Published

31-12-2014
CITATION

How to Cite

Prakasha, D., & Chavan, V. (2014). On Weak Symmetries of Generalized Sasakian-Space-Forms. Communications in Mathematics and Applications, 5(3), 83–89. https://doi.org/10.26713/cma.v5i3.249

Issue

Vol. 5 No. 3 (2014)

Section

Research Article

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