Gradient η-Ricci Solitons on ϕ-Projectively Flat Lorentzian Para-Kenmotsu Manifolds

  • Giteshwari Pandey 1. Govt. Model Science College (PMCoE), Rewa (M.P.) 486001, India
  • A. K. Mishra Department of Mathematical Sciences, A. P. S. University, Rewa (M.P.) 486003, India
  • S. K. Pandey Department of Mathematical Sciences, A. P. S. University, Rewa (M.P.) 486003, India
  • R. N. Singh Department of Mathematical Sciences, A. P. S. University, Rewa (M.P.) 486003, India
DOI: https://doi.org/10.69980/m.v12i1.6685
Keywords: Gradient η-Ricci soliton, Lorentzian para-Kenmotsu manifold, ϕ-projectively flat manifold, Einstein manifold, η-Einstein manifold, Ricci symmetric manifold

Abstract

In this paper we study gradient -Ricci solitons on -projectively flat Lorentzian para-Kenmotsu manifolds. Using the defining equation of a gradient -Ricci soliton, we investigate several geometric properties of such manifolds. First, we establish conditions under which the Ricci tensor becomes cyclic. Further, we obtain characterization results under different curvature restrictions. In particular, it is shown that if the manifold is Ricci symmetric then the soliton constants satisfy . Moreover, if the scalar curvature is constant then the manifold becomes -Einstein, and under the curvature condition  the manifold reduces to an Einstein manifold. Additional results concerning commuting Ricci operators and steady gradient -Ricci solitons are also obtained. Finally, an explicit example is constructed to illustrate the theoretical results.

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Published
2026-05-12
How to Cite
Giteshwari Pandey, A. K. Mishra, S. K. Pandey, & R. N. Singh. (2026). Gradient η-Ricci Solitons on ϕ-Projectively Flat Lorentzian Para-Kenmotsu Manifolds. IJRDO -JOURNAL OF MATHEMATICS, 12(1), 60-75. https://doi.org/10.69980/m.v12i1.6685
Issue
Vol. 12 No. 1 (2026): IJRDO - Journal Of Mathematics (ISSN: 2455-9210)
Section
Articles

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