PROJECTIVE CURVATURE TENSOR  ON ($k,\;\mu$)-CONTACT SPACE FORMS

M. Jawarneh, S. Samui, U. De

IJPAM: Volume 113, No. 3 (2017)

Title

PROJECTIVE CURVATURE TENSOR
ON ( $k,\;\mu$ )-CONTACT SPACE FORMS

Authors

M. Jawarneh $^{1}$ , S. Samui $^{2}$ , U. De $^{3}$

Department of Mathematics
AL-Kamil Faculty of Science and Arts
University of Jeddah
P.O. Box 110, Alkamil 21937, SAUDI ARABIA

Umeschandra College
Surya Sen Street, Kolkata, 700012, West Bengal, INDIA

Department of Pure Mathematics
Calcutta University
35, Ballygunge Circular Road, Kol 700019, West Bengal, INDIA

Abstract

We characterize a ( $k,\;\mu$ )-contact space form satisfying certain curvature conditions on the projective curvature tensor.

History

Received: October 14, 2016
Revised: December 26, 2016
Published: March 28, 2017

AMS Classification, Key Words

AMS Subject Classification: 53C15, 53C25.
Key Words and Phrases: (, $\mu$ )-contact space forms, N()-contact space forms, projective curvature tensor, Einstein manifolds, $\eta$ -Einstein manifolds.

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1: Akbar, A. and Sarkar, A., Some curvature properties of ( $k,\;\mu$ )-contact space forms, Malaya Journal of Matematik, 3, 1 (2015) 45-50.
2: Arslan, K., Ezentas, R., Mihai, I., Murathan, C., and Özgür, C., Certain inequalities for submanifolds in (, $\mu$ )-contact space forms, Bull. Austral. Math. Soc., 64 (2001) 201-212.
3: Blair, D.E., Contact manifolds in Riemannian geometry, Lecture notes in math., 509, Springer-verlag. (1976)
4: Blair, D.E., Koufogiorgos, T. and Papantoniou, B.J., Contact metric manifold satisfying a nullity condition, Israel J.Math. 91 (1995) 189-214.
5: Blair, D.E., Two remarks on contact metric structures, Tohoku Math. J. 29 (1977) 319-324.
6: Cabrerizo, J.L., Fernández, L.M., Fernández, M. and Zhen, G., The structure of a clss of K-contact manifolds, Acta Math. Hungar., 82, 4 (1999) 331-340.
7: De, U.C. and De, A., On some curvature properties of K-contact manifolds, Extracta Mathematicae, 27 (2012) 125-134.
8: Ghosh, S., On a class of ( $k,\;\mu$ )- contact manifolds, Bull. Cal. Math. Soc., 102 (2010) 219-226.
9: Tanno, S., Ricci curvatures of contact Riemannian manifolds, Tôhoku Math. J., 40 (1988) 441-448.
10: Koufogiorgos, T., Contact Riemannian manifolds with constant $\phi$ -sectional curvature, Tokyo J. Math., 20 (1997) 13-22.
11: Verheyen, P. and Verstraelen, L., A new intrinsic characterization of hypercylinders in Euclidean spaces, Kyungpook Math. J., 25 (1985) 1-4.
12: Yano, K. and Kon, M., Structure on manifolds, Series in Pure Mathematics 3, World Scientific Publishing Co., Singapore, (1984).
13: Yano, K. and Bochner, S., Curvature and Betti numbers, Annals of mathematics studies, 32, Princeton university press (1953).
14: Zhen, G., On conformal symmetric K-contact manifolds, Chinese Quart. J. Math., 7 (1992) 5-10.
15: Zhen, G., Cabrerizo, J.L., Fernández, L.M. and Fernández, M., On $\xi$ -conformally flat contact metric manifols, Indian J. Pure Appl. Math., 28 (1997) 725-734.

How to Cite?

DOI: 10.12732/ijpam.v113i3.5 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 3
Pages: 425 - 439

$k,\;\mu$ )-CONTACT SPACE FORMS%22&as_occt=any&as_epq=&as_oq=&as_eq=&as_publication=&as_ylo=&as_yhi=&as_sdtAAP=1&as_sdtp=1" title="Click to search Google Scholar for this entry" rel="nofollow">Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).