Rigidity of Ricci solitons for φ-related metallic semi-Riemannian structures on para-Kenmotsu manifolds
Abstract
In this paper, we investigate Ricci solitons in the para-Kenmotsu setting with respect to a φ-related metallic semi-Riemannian metric arising from the underlying almost paracontact metric structure, under the assumption that the potential vector field is pointwise collinear with the Reeb vector field. We first establish the relation tS=S+2nβ(g−η⊗η) between the Ricci tensors of the original metric g and the φ-related metallic metric tg. We then show that the Ricci soliton equation implies that the original metric g is of η-Einstein type. By combining this condition with the contracted Bianchi identity, we obtain a rigidity result implying f=0, λ=2n/C, S=−2ng, and consequently tS=−2n/Ctg. Thus, every Ricci soliton in this setting whose potential vector field is pointwise collinear with the Reeb vector field is necessarily trivial, and both g and tg are Einstein. Finally, we provide two five-dimensional para-Kenmotsu examples: one realizing the resulting trivial Einstein Ricci soliton and another showing that failure of the required Einstein condition prevents the existence of such a soliton.
Related
- Ricci Solitons, Almost Theta-Yamabe Solitons, and Finite-Order Tensor Symmetries of a Vector Field on Riemannian Manifolds with Rank-One Anisotropic Curvature
- Rigidity of volume-minimizing free boundary hypersurfaces in high dimensional Riemannian manifolds
- Paired Statistical Solitons and Torse-Forming Rigidity on Statistical Manifolds
- Intrinsic Rigidity of Bar-and-Joint Frameworks on Riemannian Manifolds
- Rigidity of nonsteady gradient Kähler-Ricci solitons with constant scalar curvature
BibTeX
@misc{karababa2026rigidity,
title = {{Rigidity of Ricci solitons for $φ$-related metallic semi-Riemannian structures on para-Kenmotsu manifolds}},
author = {Yasemin Karababa},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06535},
eprint = {2611.06535},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06535},
}
RIS
TY - UNPB
TI - Rigidity of Ricci solitons for φ-related metallic semi-Riemannian structures on para-Kenmotsu manifolds
AU - Yasemin Karababa
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06535
UR - https://arxiv.org/abs/2611.06535
AB - In this paper, we investigate Ricci solitons in the para-Kenmotsu setting with respect to a φ-related metallic semi-Riemannian metric arising from the underlying almost paracontact metric structure, under the assumption that the potential vector field is pointwise collinear with the Reeb vector field. We first establish the relation tS=S+2nβ(g−η⊗η) between the Ricci tensors of the original metric g and the φ-related metallic metric tg. We then show that the Ricci soliton equation implies that the original metric g is of η-Einstein type. By combining this condition with the contracted Bianchi identity, we obtain a rigidity result implying f=0, λ=2n/C, S=−2ng, and consequently tS=−2n/Ctg. Thus, every Ricci soliton in this setting whose potential vector field is pointwise collinear with the Reeb vector field is necessarily trivial, and both g and tg are Einstein. Finally, we provide two five-dimensional para-Kenmotsu examples: one realizing the resulting trivial Einstein Ricci soliton and another showing that failure of the required Einstein condition prevents the existence of such a soliton.
ER -