Generalized Sasakian space forms with $m$-projective curvature
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Abstract
In the present paper, we have studied ϕ-m-projectively flat generalized Sasakian space forms, m-projectively locally symmetric generalized Sasakian space form and m-projectively locally ϕ-symmetric generalized Sasakian space forms. Obtained results are supported by illustrative examples.
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Singh, J.
(2016).
Generalized Sasakian space forms with $m$-projective curvature.
Acta Mathematica Universitatis Comenianae, 85(1), 135-146.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/217/294
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References
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[2] Alegre P. and Carriazo A., Structures on generalised Sasakian space forms, Diff. Geom. Appl. 26 (2008), 656-666.
[3] Blair D.E.,Contact manifolds in Riemannian Geometry, Lecture notes in Mathematics, 509, Springer-Verlag, Berlin, 1976.
[4] Chaubey S. K. and Ojha R. H.,On the M-projective curvature tensor of a Kenmotsu manifolds, Diff. Geom.-Dynamical Systems, 12(2010) 52-60.
[5] De U.C. and Sarkar A., On the projective curvature tensor of generalized Sasakian space forms, Quaestiones Math. 33 (2010), 245-252.
[6] De U.C. and Sarkar A., Some curvature properties of generalized Sasakian space forms,Lob.J. of Math.,33(1), (2012),22-27.
[7] De U.C., Singh R.N. and Pandey S.K.,On the conharmonic curvature tensor of generalized Sasakian space forms,Int. Sch. Res. Network,ISRN Geometry, 8 (2010), 1-10.
[8] Golab S., On semi-symmetric and quarter-symmetric linear conncetions, Tensor (N.S) 29 (1975),249-254.
[9] Kim U. K., conformally flat generalised sasakian space forms and locally symmetric generalised Sasakian space forms, Note di mathematica, 26 (2006),55-67.
[10] Ojha R. H., A note on the m-projective curvature tensor, Indian J. Pure appl. Math. 8(12) (1975), 1531-1534.
[11] Ojha R. H.,On Sasakian manifold, Kyungpook Math. J. 13 (1973), 211-215. [12] Ozgur C., On ϕ-conformally flat LP-Sasakian manifolds, Rad. Mat. 12 (2003), 99-106.
[13] Pokhariyal G. P. and Mishra R.S., Curvature tensor and their relativistic significance II, Yokohama Mathematical Journal 19 (1971), 97-103.
[14] Singh J. P., On an Einstein m-projective P-Sasakian manifolds. Bull. Cal. Math. Soc., 101(2) (2009), 175-180.
[15] Singh J. P. ,On m-projective recurrent Riemannian manifold. Int. J. of Math. Analysis, 24(6) ( 2012), 1173-1178.
[16] Sarkar A.and Akbar A., Generalised sasakian space forms with projective curvature tensor, Demonstratio Mathematica, XLVII(3)(2014),725-735.
[17] Venkatesha and Sumangala B., On M-projective curvature tensor of a generalised Sasakian space form, Acta math. Univ. Comenianae, LXXXII(2) (2013),209-217.
[2] Alegre P. and Carriazo A., Structures on generalised Sasakian space forms, Diff. Geom. Appl. 26 (2008), 656-666.
[3] Blair D.E.,Contact manifolds in Riemannian Geometry, Lecture notes in Mathematics, 509, Springer-Verlag, Berlin, 1976.
[4] Chaubey S. K. and Ojha R. H.,On the M-projective curvature tensor of a Kenmotsu manifolds, Diff. Geom.-Dynamical Systems, 12(2010) 52-60.
[5] De U.C. and Sarkar A., On the projective curvature tensor of generalized Sasakian space forms, Quaestiones Math. 33 (2010), 245-252.
[6] De U.C. and Sarkar A., Some curvature properties of generalized Sasakian space forms,Lob.J. of Math.,33(1), (2012),22-27.
[7] De U.C., Singh R.N. and Pandey S.K.,On the conharmonic curvature tensor of generalized Sasakian space forms,Int. Sch. Res. Network,ISRN Geometry, 8 (2010), 1-10.
[8] Golab S., On semi-symmetric and quarter-symmetric linear conncetions, Tensor (N.S) 29 (1975),249-254.
[9] Kim U. K., conformally flat generalised sasakian space forms and locally symmetric generalised Sasakian space forms, Note di mathematica, 26 (2006),55-67.
[10] Ojha R. H., A note on the m-projective curvature tensor, Indian J. Pure appl. Math. 8(12) (1975), 1531-1534.
[11] Ojha R. H.,On Sasakian manifold, Kyungpook Math. J. 13 (1973), 211-215. [12] Ozgur C., On ϕ-conformally flat LP-Sasakian manifolds, Rad. Mat. 12 (2003), 99-106.
[13] Pokhariyal G. P. and Mishra R.S., Curvature tensor and their relativistic significance II, Yokohama Mathematical Journal 19 (1971), 97-103.
[14] Singh J. P., On an Einstein m-projective P-Sasakian manifolds. Bull. Cal. Math. Soc., 101(2) (2009), 175-180.
[15] Singh J. P. ,On m-projective recurrent Riemannian manifold. Int. J. of Math. Analysis, 24(6) ( 2012), 1173-1178.
[16] Sarkar A.and Akbar A., Generalised sasakian space forms with projective curvature tensor, Demonstratio Mathematica, XLVII(3)(2014),725-735.
[17] Venkatesha and Sumangala B., On M-projective curvature tensor of a generalised Sasakian space form, Acta math. Univ. Comenianae, LXXXII(2) (2013),209-217.