Qausi Conformal Curvature Tensor on N(k)-Contact Metric Manifold
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Abstract
The purpose of this paper is to study N(k)-contact metric manifold endowed with a qausi-conformal curvature tensor. Here we consider quasiconformally flat, Einstein semi-symmetric quasi-conformally flat, quasi- conformally semi-symmetric and globally -quasiconformally symmetric N(k)-contact metric manifold.
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Venkatesha, ?., & Kumar, R.
(2016).
Qausi Conformal Curvature Tensor on N(k)-Contact Metric Manifold.
Acta Mathematica Universitatis Comenianae, 85(1), 125-134.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/215/293
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References
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[11] U.C. De, Kae Bok Jun and Abul Kalam Gazi, Sasakian manifolds with quasi-conformal curvature tensor, Bull. Korean Math. Soc., 45 (2008), No. 2, 313-319.
[12] U.C. De and Y. Matsuyama, On quasi-conformally flat manifolds, SUT. J. Math., 42 (2), 295 (2006).
[13] D.G. Prakasha, C.S. Bagewadi and Venkatesha, Conformally and quasi-conformally conservative curvature tensors on a trans-Sasakian manifold with respect to semi-symmetric metric connections, Differential Geometry - Dynamical Systems, Vol.10, (2008), 263-274.
[14] Rajendra Prasad and Pankaj, On (k, µ)-Manifolds with Quasi-Conformal Curvature Tensor, Int. J. Contemp. Math. Sciences, Vol. 5, (2010), no. 34, 1663-1676.
[15] Sujit Ghosh and U.C. De, On \pfi-Quasiconformally Symmetric (k, )-Contact Manifolds, Lobachevskii Journal of Mathematics, Vol. 31, No. 4, (2010), 367375.
[16] Z.I. Szabo, Structure theorems on Riemannian space satisfying R(X, Y ).R = 0, I, The local version, J. Differential Geom., 17, 531 (1982).
[17] S. Tanno, Locally symmetric K-contact Riemannian manifolds, Proc. Japan Acad., 43, 581 (1967).
[18] S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tohoku Mathematical journal, 40, 441
(1988).
[19] K. Yano and M. Kon, Structures on Manifolds, Vol. 3 of Series in Pure Mathematics, World Scientific, Singapore, (1984).
[20] K. Yano and S. Sawaki, Riemannian Manifolds Admitting a Conformal Transformation Group, J. Diff. Geom., 2, 161 (1968).
[2] Ahmet Yildiz and U.C. De, A classification of (k, \mu)-Contact Metric Manifolds, Commun. Korean Math,
Soc., 27 (2012), 327-339.
[3] D.E. Blair, Contact manifolds in Riemannian geometry. Lecture Notes in Math., No. 509, Springer, 1976.
[4] D.E. Blair, Two remarks on contact metric structures., Tohoku Math. J., 29 (1977), 319-324.
[5] D.E. Blair, J.S. Kim and M.M. Tripathi, On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc., 42 (2005), 883-892.
[6] D.E. Blair, T. Koufogiorgos and Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91, 189 (1995).
[7] E. Boeckx, A full classification of contact metric (k, µ)-spaces, Illinois J. Math., 44 (1), 212 (2000).
[8] W.M. Boothby and H.C. Wang, On contact manifolds, Ann. of Math., 68 (1958), 721-734.
[9] Cihan Ozgur and U.C. De, On the quasi-conformal curvature tensor of a kenmotsu manifold, Mathematica
Pannonica, 17(2) (2006), 221-228.
[10] U.C. De and Avijit Sarkar, On the quasi-conformal curvature tensor of a (k, µ)-contact metric manifold, Math.. Reports 14 (64), 2 (2012), 115-129.
[11] U.C. De, Kae Bok Jun and Abul Kalam Gazi, Sasakian manifolds with quasi-conformal curvature tensor, Bull. Korean Math. Soc., 45 (2008), No. 2, 313-319.
[12] U.C. De and Y. Matsuyama, On quasi-conformally flat manifolds, SUT. J. Math., 42 (2), 295 (2006).
[13] D.G. Prakasha, C.S. Bagewadi and Venkatesha, Conformally and quasi-conformally conservative curvature tensors on a trans-Sasakian manifold with respect to semi-symmetric metric connections, Differential Geometry - Dynamical Systems, Vol.10, (2008), 263-274.
[14] Rajendra Prasad and Pankaj, On (k, µ)-Manifolds with Quasi-Conformal Curvature Tensor, Int. J. Contemp. Math. Sciences, Vol. 5, (2010), no. 34, 1663-1676.
[15] Sujit Ghosh and U.C. De, On \pfi-Quasiconformally Symmetric (k, )-Contact Manifolds, Lobachevskii Journal of Mathematics, Vol. 31, No. 4, (2010), 367375.
[16] Z.I. Szabo, Structure theorems on Riemannian space satisfying R(X, Y ).R = 0, I, The local version, J. Differential Geom., 17, 531 (1982).
[17] S. Tanno, Locally symmetric K-contact Riemannian manifolds, Proc. Japan Acad., 43, 581 (1967).
[18] S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tohoku Mathematical journal, 40, 441
(1988).
[19] K. Yano and M. Kon, Structures on Manifolds, Vol. 3 of Series in Pure Mathematics, World Scientific, Singapore, (1984).
[20] K. Yano and S. Sawaki, Riemannian Manifolds Admitting a Conformal Transformation Group, J. Diff. Geom., 2, 161 (1968).