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

U.c. De; Srimayee Samui

doi:10.36753/mathenot.421477

EN

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

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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

U.c. De

Srimayee Samui This is me

Publication Date

April 30, 2017

Submission Date

August 20, 2016

Acceptance Date

-

Published in Issue

Year 2017 Volume: 5 Number: 1

DOI

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

IZ

https://izlik.org/JA84XS79WH

APA

De, U., & Samui, S. (2017). On a Subclass of (k, µ)-Contact Metric Manifolds. Mathematical Sciences and Applications E-Notes, 5(1), 9-18. https://doi.org/10.36753/mathenot.421477

AMA

1.De U, Samui S. On a Subclass of (k, µ)-Contact Metric Manifolds. Math. Sci. Appl. E-Notes. 2017;5(1):9-18. doi:10.36753/mathenot.421477

Chicago

De, U.c., and Srimayee Samui. 2017. “On a Subclass of (k, µ)-Contact Metric Manifolds”. Mathematical Sciences and Applications E-Notes 5 (1): 9-18. https://doi.org/10.36753/mathenot.421477.

EndNote

De U, Samui S (April 1, 2017) On a Subclass of (k, µ)-Contact Metric Manifolds. Mathematical Sciences and Applications E-Notes 5 1 9–18.

IEEE

[1]U. De and S. Samui, “On a Subclass of (k, µ)-Contact Metric Manifolds”, Math. Sci. Appl. E-Notes, vol. 5, no. 1, pp. 9–18, Apr. 2017, doi: 10.36753/mathenot.421477.

ISNAD

De, U.c. - Samui, Srimayee. “On a Subclass of (k, µ)-Contact Metric Manifolds”. Mathematical Sciences and Applications E-Notes 5/1 (April 1, 2017): 9-18. https://doi.org/10.36753/mathenot.421477.

JAMA

1.De U, Samui S. On a Subclass of (k, µ)-Contact Metric Manifolds. Math. Sci. Appl. E-Notes. 2017;5:9–18.

MLA

De, U.c., and Srimayee Samui. “On a Subclass of (k, µ)-Contact Metric Manifolds”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 1, Apr. 2017, pp. 9-18, doi:10.36753/mathenot.421477.

Vancouver

1.U.c. De, Srimayee Samui. On a Subclass of (k, µ)-Contact Metric Manifolds. Math. Sci. Appl. E-Notes. 2017 Apr. 1;5(1):9-18. doi:10.36753/mathenot.421477