$\rho$-Einstein solitons in Lorentzian para-Kenmotsu manifolds


Abstract views: 174 / PDF downloads: 151

Authors

  • Mobin Ahmad Integral University's
  • Mohd. Bilal Umm Al Qura University
  • Gazala Integral University

Keywords:

$\rho$-Einstein soliton;, Einstein manifolds;, Lorentzian para-Kenmotsu manifolds

Abstract

The main purpose of the current paper is to study certain curvature conditions in Lorentzian para-Kenmotsu $n$-manifolds (briefly, $(LPK)_n$) admitting $\rho$-Einstein solitons ($\rho$-ES).

Author Biographies

Mohd. Bilal, Umm Al Qura University

Department of Mathematical Sciences, 
Faculty of Applied Sciences

Gazala, Integral University

Department of Mathematics & Statistics,

Faculty of Science

References

Ahmad, M., Gazala and Al-Shabrawi, M. A., A note on $LP$-Kenmotsu manifolds admitting conformal Ricci-Yamabe solitons, Int. J. Anal. Appl., 21 (2023), 32, 1-12.

Bourguignon, J. P., Ricci curvature and Einstein metrics, Global differential geometry and global analysis, Lecture notes in Math., 838 (1981), 42-63.

Bourguignon, J. P. and Lawson, H. B., Stability and isolation phenomena for Yang-mills fields, Commun. Math. Phys., 79 (1981), 189-230.

Catino, G., Cremaschi, L., Djadli, Z., Mantegazza, C. and Mazzieri, L., The Ricci-Bourguignon flow, Pacific J. Math., 287(2017), 333-370.

De, U. C. and Majhi, P., $varphi$-semisymmetric generalized Sasakian space-forms, Arab J. Math. Sci., 21 (2015), 170-178.

Hamilton, R. S., The Ricci Flow on Surfaces, Mathematics and General Relativity (Santa Cruz, CA, 1986), Contemp. Math., A.M.S., 71 (1988), 237-262.

Haseeb, A., Chaubey, S. K., Mofarreh, F. and Ahmadini, A. A. H., A solitonic study of Riemannian manifolds equipped with a semi-symmetric metric $xi$-connection. Axioms, 12(9) (2023), 1-11.

Haseeb, A. and Prasad, R., Certain results on Lorentzian para-Kenmotsu manifolds, Bol. Soc.

Parana. Mat., 39(3) (2021), 201-220.

Haseeb, A. and Prasad, R., Some results on Lorentzian para-Kenmotsu manifolds, Bull. Transilvania Univ. Brasov. 13(62) (2020), 185-198.

Ishii, Y., On conharmonic transformations, Tensor (N. S.), 7 (1957), 73-80.

Prasad, R. and Haseeb, A., On Lorentzian para-Sasakian manifold with respect to the quarter-symmetric metric connection, {Novi Sad J. Math.}, 62(2) (2016), 103-116.

Shaikh, A. A. and Biswas, S., On $LP$-Sasakian manifolds, Bull Malaysian Math. Sci. Soc., 27 (1)(2004), 17-26.

Mishra, R. S., Structures on a differentiable manifold and their applications; Chandrama Prakashan: Allahabad, India, 1984.

Mondal, C. K. and Shaikh, A. A., Some results on $eta$-Ricci Soliton and gradient $rho$-Einstein soliton in a complete Riemannian manifold, Commun. Korean Math. Soc., 34(4) (2019), 1279-1287.

Patra, D. S, Some characterizations of $rho$-Einstein solitons on Sasakian manifolds, Canadian Mathematical Bulletin, (2022), 1-14.

Shaikh, A. A., Cunha, A. W. and Mandal, P., Some characterizations of $rho$-Einstein solitons, Journal of Geometry and Physics, vol. 166, Article ID 104270, 2021.

Shaikh, A. A., Mandal, P and Mondal, C. K., Diameter estimation of gradient $rho$-Einstein solitons, Journal of Geometry and Physics, vol. 177, Article ID 104518, 2022.

Suh, Y. J., Ricci-Bourguignon solitons on real hypersurfaces in the complex hyperbolic quadric, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 116 (2022).

O'Neill, B., Semi-Riemannian geometry with applications to relativity, {Academic Press}, New York, 1983.

Matsumoto, K., On Lorentzian paracontact manifolds, {Bull. Yamagata Univ. Natur. Sci.}, 12(1989), 151-156.

Haseeb, A., Chaubey, S. K. and Khan, M.A., Riemannian 3-manifolds and Ricci-Yamabe solitons, { Int. J. Geom. Methods Mod. Phys.}, 20(1)(2023), 2350015

Singh, J. P. and Khatri, M., On Ricci-Yamabe soliton and geometrical structure in a perfect fluid spacetime, {Afr. Mat.}, 32(2021), 1645-1656.

{ Yoldas, H. I.}, {On Kenmotsu manifolds admitting $ eta$-Ricci-Yamabe solitons}, {Int. J. Geom. Methods Mod. Phys.}, 18(2021), 2150189.

Yano, K., On torse-forming direction in Riemannian space, Proc. Imp. Acad. Tokyo 20(1944), 340-345.

Downloads

Published

2024-06-03

How to Cite

Ahmad, M., Mohd. Bilal, & Gazala. (2024). $\rho$-Einstein solitons in Lorentzian para-Kenmotsu manifolds. Results in Nonlinear Analysis, 7(2), 53–63. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/391

Most read articles by the same author(s)