Certain results on the conharmonic curvature tensor of \( (\kappa,\mu) \)-contact metric manifolds

G. Divyashree; Venkatesha

doi:10.4067/S0719-06462020000100071

DOI:

https://doi.org/10.4067/S0719-06462020000100071

Abstract

The paper presents a study of \( (\kappa,\mu) \)-contact metric manifolds satisfying certain conditions on the conharmonic curvature tensor.

Keywords

\( (\kappa,\mu) \)-contact metric manifold , conharmonically flat , conharmonically locally \(\phi\)-symmetric , \(\phi\)-conharmonically semisymmetric , \(h\)-conharmonically semisymmetric

G. Divyashree Department of Mathematics, Govt., Science College, Chitradurga-577501, Karnataka, India.
Venkatesha Department of Mathematics, Kuvempu University, Shankaraghatta - 577 451, Shimoga, Karnataka, India.

Pages: 71–84
Date Published: 2020-04-18
Vol. 22 No. 1 (2020)

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

D. E. Blair, Two remarks on contact metric structures, Tohoku Math. J., 29, pp. 319-324, 1977.

D.E. Blair, T. Koufogiorgos and B.J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math., 19, pp. 189-214, 1995.

E. Boeckx, A full classification of contact metric (Îº, Î¼)-spaces, Illinois J. of Math. 44, pp. 212-219, 2000.

A. Ghosh, R. Sharma and J.T. Cho, Contact metric manifolds with Î·-parallel torsion tensor, Ann. Glob. Anal Geom. 34, pp. 287-299, 2008.

Jun J. B. Yildiz A. and De U. C, On Ï†-recurrent (Îº, Î¼)contact metric manifolds, Bull. Korean Math. Soc. 45, pp. 689-700, 2008.

Nader Asghari and Abolfazl Taleshian, On the Conharmonic curvature tensor of Kenmotsu manifolds, Thai Journal of Mathematics, 12(3), pp. 525-536, 2014.

C. Özgür, On Ï†-conformally flat Lorentzian para-Sasakian manifolds, Radovi Matematicki, 12(1), pp. 99-106, 2003.

D. Perrone, Homogeneous contact Riemannian three-manifolds, Illinois J. Math. 42, pp. 243-258, 1998.

A. Sarkar, Matilal Sen and Ali Akbar, Generalized Sasakian space forms with conharmonic curvature tensor, Palestine Journal of Mathematics, 4(1), pp. 84-90, 2015.

A. A. Shaikh and K. Kanti Baishya, On (Îº, Î¼)-contact metric manifolds, Differential Geometry Dynamical Systems, 8, pp. 253-261, 2006.

S. A. Siddiqui and Z. Ahsan, Conharmonic curvature tensor and the space-time of general relativity, Differential Geometry-Dynamical Systems, 12, pp. 213-220, 2010.

A. Yildiz and U. C. De, A classification of (Îº, Î¼)-contact metric manifolds, Commun. Korean Math. Soc., 2, pp. 327-339, 2012.