On The Ricci Symmetry of Almost Kenmotsu Manifolds

Article Sidebar

PDF
Published: Aug 1, 2022
DOI: https://doi.org/10.5556/j.tkjm.53.2022.3761
Keywords:
Almost Kenmotsu manifolds Ricci symmetric manifolds Einstein manifold Sectional curvature

Main Article Content

Dibakar Dey
University of Calcutta

Abstract




In the present paper, we characterize Ricci symmetric almost Kenmotsu manifolds under several constraints and proved that they are Einstein manifolds. As a consequence, we obtain several corollaries. Finally, an illustrative example is presented to verify our results.




Article Details

How to Cite
Dey, D. (2022). On The Ricci Symmetry of Almost Kenmotsu Manifolds. Tamkang Journal of Mathematics, 53(3), 229–238. https://doi.org/10.5556/j.tkjm.53.2022.3761
Issue
Vol. 53 No. 3 (2022)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

D. E. Blair, Contact manifold in Riemannian Geometry. Lecture Notes on Mathematics, Springer, Berlin, 509(1976).

D. E. Blair, Riemannian Geometry on contact and symplectic manifolds, Progr. Math., Birkhäuser, Boston, 203(2010).

E. Cartan, Sur une classes remarquable d’espaces de Riemannian, Bull. Soc. Math. France 54(1926), 214-264.

U. C. De and D. Dey, Pseudo-symmetric structures on almost Kenmotsu manifolds with nullity distributions, Acta Comment. Univ. Tartu. Math. 23(2019), 13-24.

G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93(2009), 46-61.

G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds with a condition of η-parallelsim, Differential Geom. Appl. 27(2009), 671-679.

G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin, 14(2007), 343-354.

S. Deshmukh, U. C. De and P. Zhao, Ricci semisymmetric almost Kenmotsu manifolds with nullity distributions, Filomat 32(2018), 179-786.

D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J. 4(1981), 1-27.

G. Ghosh and P. Majhi, Certain results on almost Kenmotsu manifolds with conformal Reeb foliation, Commun. Korean Math. Soc. 33(2018), 261-272.

K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24(1972), 93-103.

B. O’Neill, Semi-Riemannian Geometry, Academic Press, Inc. NY 1983.

A. M. Pastore and V. Saltarelli, Generalized nullity distribution on almost Kenmotsu manifolds, Int. Elec. J. Geom. 4(2011), 168-183.

A. M. Pastore and V. Saltarelli, Almost Kenmotsu manifolds with conformal Reeb foliation, Bull. Belg. Math. Soc. Simon Stevin 21 (2012), 343-354.

R. Sharma, On the curvature of contact metric manifolds, J. Geom. 53(1995), 179-190.

Y. Wang, Three dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math. 116(2016), 79-86.