H-almost Ricci-Yamabe solitons in paracontact geometry

TL;DR

The work classifies h-almost Ricci-Yamabe solitons and their gradient analogues on paracontact geometries, deriving structural constraints that force η-Einstein or Einstein conditions across para-Kenmotsu, para-Sasakian, and para-cosymplectic manifolds. A key finding is that proper h-ARYS typically yield η-Einstein or Einstein manifolds, with 3D para-Sasakian cases further collapsing to space forms of negative curvature (H^3(1)). In the gradient setting, constant scalar curvature in 3D often reduces h-AGRYS to h-gradient Ricci-Yamabe solitons, accompanied by constant soliton parameters. The paper also provides two explicit 3D examples to illustrate the theoretical classifications and parameter relations among $h$, $\alpha$, $\beta$, $\lambda$, and $r$, enriching concrete models in paracontact geometry.

Abstract

In this article, we classify h-almost Ricci-Yamabe solitons in paracontact geometry. In particular, we characterize para-Kenmotsu manifolds satisfying h-almost Ricci-Yamabe solitons and 3-dimensional para-Kenmotsu manifolds obeying h-almost gradient Ricci-Yamabe solitons. Next, we classify para-Sasakian manifolds admitting h-almost Ricci-Yamabe solitons and h-almost gradient Ricci-Yamabe solitons. Besides these, we investigate h-almost Ricci-Yamabe solitons and h-almost gradient Ricci-Yamabe solitons in para-cosymplectic manifolds. Finally, we construct two examples to illustrate our results.

Theorems & Definitions (12)

• Lemma 2.1
• Theorem 3.1
• Theorem 3.2
• Lemma 4.1
• Theorem 5.1
• Corollary 5.1
• Theorem 5.2
• Lemma 6.1
• Lemma 6.2
• Theorem 7.1