ON m-PROJECTIVE CURVATURE TENSOR OF GENERALIZED SASAKIAN-SPACE-FORMS
Abstract
The object of the present paper is to characterize generalized Sasakian-space-forms satisfying certain curvature conditions on m-projective curvature tensor. In this paper, we study m-projectively semisymmetric, m-projectively flat, $\xi$-m-projectively flat, m-projectively recurrent generalized Sasakian-space-forms. Also $W^*.S = 0$ and $W^*.R= 0$ on generalized Sasakian-space-forms are studied.
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begin{thebibliography}{00}
bibitem{ABC} P. Alegre, D. E. Blair and A. Carriazo, textit{Generalized Sasakian-space-forms,} Israel J. Math., {bf141}(2004),151-183.
bibitem{AC} P.Alegre and A.Carriazo,textit{Structures on generalized Sasakian-space-forms,} Differential Geom. and its Application, {bf26}(2008), 656-666.doi 10.1016/J.difgeo.
bibitem{ACKY}P.Alegre, A.Carriazo, Y.H.Kim and D.W.Yoon,textit{B.Y.Chen's innequality for submanifolds of generalized space forms,} Indian J. Pure Appl. Math., {bf38}(2007), 185-201.
bibitem{GHSOSH} R.Al-Ghefari, F. R. Al-Solamy and M.H.Shahid, textit{CR-Submanifolds of generalized Sasakian-space-forms,} JP J. Geom.Topol., {bf6}(2006), 151-166.
bibitem{GHSOSHD} R.Al-Ghefari, F.R. Al-Solamy and M.H.Shahid, textit{Contact CR-warped product submanifolds in generalized Sasakian-space-forms,} Balkan J. Geom., Appl., {bf11(2)}(2006), 1-10.
bibitem{BLA} D. E. Blair,textit{Contact manifolds in a Riemannian geometry,} Lecture notes in Math., 509, Springer Verlag, Verlin, (1976).
bibitem{DESAR} U. C. De and Avijit Sarkar, textit{On the projective curvature tensor of generalized Sasakian-space-forms,} Quaestiones Mathematicae, {bf33}(2010), 245-252.
bibitem {DSP} U. C. De, R. N. Singh and S. K. Pandey, textit{On the conharmonic curvature tensor of generalized Sasakian-space-forms,}ISRN Geometry, 14 Pages, doi:10.5402/2012/876276, 2012.
bibitem{KIM} U. K. Kim, textit{Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms,} Note di Mathematica,{bf26}(2006), 55-67.
bibitem{OJH}R. H. Ojha, textit{M-Projectively flat Sasakian manifolds,} Indian J. Pure Appl. Math.,{bf17(4)}(1986), 481-484.
bibitem{OZG}C.$ddot{O}$zg$ddot{u}$r, textit{On $phi$- conformally flat Lorentzian para Sasakian manifolds,} Radovi Mathematicki,{bf12(1)}(2003), 99-106.
bibitem{POM}G. P. Pokhariyal and R. S. Mishra, textit{Curvature tensor and their relativistic significance II,} Yokohama Mathematical Journal,{bf19}(1971), 97-103.
bibitem{POL}E. A. Polkina, textit{Curvature identities for almost contact metric manifolds,} Russian Mathematics (IZ VUZ),{bf51(7)}(2007), 54-57.
bibitem{ZCFF}G. Zhen, J. L. Cabrerizo, L. M. Fern$acute{a}$ndez and M. Fern$acute{a}$ndez, textit{On $xi$-conformally flat contact metric manifolds,} Indian J.Pure Appl. Math.,{bf28}(1997), 725-734.
end{thebibliography}
DOI: https://doi.org/10.22190/FUMI1803361P
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