https://neckpinch.com/authors/yasemin-karababa/New arXiv papers by Yasemin Karababa, from Neckpinch Sat, 07 Nov 2026 18:19:38 GMT https://neckpinch.com/papers/2611.06535/arxiv:2611.06535Wed, 04 Nov 2026 00:00:00 GMTYasemin Karababa — 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+2nβbigl(g-η⊗ηbigr) 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.Ricci solitonsStability & uniquenessSasakian & contact geometry