On a Subclass of (k, µ)-Contact Metric Manifolds

Year 2017, Volume: 5 Issue: 1, 9 - 18, 30.04.2017

U.c. De , Srimayee Samui

https://doi.org/10.36753/mathenot.421477

Abstract

The object of this paper is to characterize (k, µ)-contact metric manifolds satisfying certain curvature
conditions on the contact conformal curvature tensor. 

Keywords

(k˒ µ)-contact metric manifolds , N(k)-contact metric manifolds , contact conformal curvature tensor , extended contact conformal curvature tensor , η-Einstein manifolds

References

• [1] Blair, D.E., Koufogiorgos T. and Papantoniou B. J., Contact metric manifold satisfying a nullity condition, Israel J.Math., 91(1995), 189 − 214.
• [2] Blair, D. E., Kim, J. S. and Tripathi, M. M.,On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc., 42(2005), 883-892.
• [3] Blair, D.E, Two remarks on contact metric structures, Tohoku Math. J., 29(1977), 319 − 324.
• [4] Boothby, W. M. and Wang, H. C., On contact manifolds, Ann of Math., 68(1958), 721 − 734.
• [5] De, U.C and Sarkar, A., On Quasi-conformal curvature tensor of (k, µ)-contact metric manifold, Math. Reports, 14(64), 2(2012), 115 − 129.
• [6] Ghosh, S. and De, U. C., On φ-Quasiconformally symmetric (k, µ)-contact metric manifolds, Lobachevskii Journal of Mathematics, 31(2010), 367 − 375.
• [7] Jun, J.B., Yildiz, A. and De, U.C.,On φ-recurrent (k, µ)-contact metric manifolds, Bull. Korean Math. Soc. 45(4)(2008), 689.
• [8] Jeong, J. C., Lee, J. D., Oh, G. H. and Pak, J. S., A note on the contact conformal curvature tensor, Bull. Korean Math. Soc., 27(1990), 133 − 142.
• [9] Kang, T. H. and Pak, J. S., Some remarks for th spectrum of the p-Laplacian on Sasakian manifolds, J. Korean Math. Soc., 32(1995), 341 − 350.
• [10] Kim, J. S., Choi, J., Özgür, C. and Tripathi, M. M.,On the Contact conformal curvature tensor of a contact metric manifold, Indian J. pure appl. Math., 37(4)(2006), 199 − 206.
• [11] Kitahara, H., Matsuo, K. and Pak, J. S., A conformal curvature tensor field on Hermitian manifolds, J. Korean Math. Soc., 27(1990), 27 − 30.
• [12] Kuhnel, W., Conformal transformations between Einstein spaces, Conformal geometry (Bonn, 1985/1986), 105-146, Asepects math., E12, Vieweg, Braunschweig, 1988.
• [13] Papantoniou, B.J., Contact Riemannian manifolds satisfying R(ξ, X) · R = 0 and ξ ∈ (k, µ)-nullity distribution, Yokohama Math.J., 40(1993), 149 − 161.
• [14] Pak, J. S., Jeong, J. C. and Kim, W. T., The contact conformal curvature tensor field and the spectrum of the Laplacian, J. Korean. Math. Soc., 28(1991), 267 − 274.
• [15] Pak, J. S. and Shin, Y. J., A note on contact conformal curvature tensor, Commun. Korean Math. Soc., 13(2)(1998), 337 − 343.
• [16] Tanno, S., Ricci curvatures of contact Riemannian manifolds, Tôhoku Math. J., 40(1988), 441 − 448 .
• [17] Yano, K., Concircular geometry I. concircular transformations, Proc. Imp. Acad. Tokyo, 16(1940), 195-200.
• [18] Yildiz, A. and De, U. C., A classification of (k, µ)-contact metric manifolds, Commun. Korean Math. Soc., 27(2012), 327-339.