Gradient ρ-Einstein and Quasi-Yamabe Solitons on Para-Kenmotsu Manifolds with Adapted Connections
- 1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai 600127, India
- 2Department of Mathematics, Sidho-Kanho-Birsha University, Purulia 723104, India
- 3Department of Computer Engineering, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia
Abstract
We investigate gradient ρ-Einstein solitons and quasi-Yamabe solitons on η-Einstein para-Kenmotsu manifolds, with particular emphasis on the Zamkovoy and Schouten–van Kampen connections. For gradient ρ-Einstein solitons, we derive a curvature identity and establish a rigidity alternative: either the scalar curvature is constant or the potential vector field is pointwise collinear with the Reeb vector field. The proof treats the possible zero set of the coefficient arising in the key pointwise identity. For quasi-Yamabe solitons with a Reeb-collinear potential vector field, we show that the scalar curvature associated with either adapted connection equals the soliton constant σ. The curvature calculations give r˜=r*=r+2n(2n+1), and hence r=σ−2n(2n+1) in this case. The coefficient h in V=hζ satisfies dh=μh2η for both connections. In particular, μ=0 makes h constant on each connected component and reduces the quasi-Yamabe soliton equation to the corresponding adapted Yamabe-type soliton equation. We also clarify the connection-dependent symmetric metric-deformation tensor and distinguish its vanishing from the classical Killing condition. These results describe the restrictions imposed by the para-Kenmotsu structure and the chosen adapted connection on the soliton equations.
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BibTeX
@article{roy2026gradient,
title = {{Gradient ρ-Einstein and Quasi-Yamabe Solitons on Para-Kenmotsu Manifolds with Adapted Connections}},
author = {Soumendu Roy and Jhantu Das and Mohammad Nazrul Islam Khan},
journal = {Axioms},
year = {2026},
month = nov,
doi = {10.3390/axioms15110833},
url = {https://www.mdpi.com/2075-1680/15/11/833},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Gradient ρ-Einstein and Quasi-Yamabe Solitons on Para-Kenmotsu Manifolds with Adapted Connections
AU - Soumendu Roy
AU - Jhantu Das
AU - Mohammad Nazrul Islam Khan
PY - 2026
DA - 2026/11/07
JO - Axioms
DO - 10.3390/axioms15110833
UR - https://www.mdpi.com/2075-1680/15/11/833
AB - We investigate gradient ρ-Einstein solitons and quasi-Yamabe solitons on η-Einstein para-Kenmotsu manifolds, with particular emphasis on the Zamkovoy and Schouten–van Kampen connections. For gradient ρ-Einstein solitons, we derive a curvature identity and establish a rigidity alternative: either the scalar curvature is constant or the potential vector field is pointwise collinear with the Reeb vector field. The proof treats the possible zero set of the coefficient arising in the key pointwise identity. For quasi-Yamabe solitons with a Reeb-collinear potential vector field, we show that the scalar curvature associated with either adapted connection equals the soliton constant σ. The curvature calculations give r˜=r*=r+2n(2n+1), and hence r=σ−2n(2n+1) in this case. The coefficient h in V=hζ satisfies dh=μh2η for both connections. In particular, μ=0 makes h constant on each connected component and reduces the quasi-Yamabe soliton equation to the corresponding adapted Yamabe-type soliton equation. We also clarify the connection-dependent symmetric metric-deformation tensor and distinguish its vanishing from the classical Killing condition. These results describe the restrictions imposed by the para-Kenmotsu structure and the chosen adapted connection on the soliton equations.
SN - 2075-1680
ER -