2025/11/06 by Santu Dey, Biswas, Rajdip, Dey, Santu +2
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Contact Mechanics and Variational Inequalities
paper · pdf · doi:10.48550/arxiv.2511.04165
In this article, we studied δ-almost Yamabe solitons within the framework of para- contact metric manifolds. First, we proved that for a paracontact metric manifold M, if a paracontact metric g represents a δ-almost Yamabe soliton associated with the potential vector field Z being an infinitesimal contact transformation, then Z is Killing and if the potential vector field Z is collinear with ξ, then the manifold M is K-paracontact. Next, if we take a K-paracontact metric mani- fold admitting δ-almost Yamabe soliton with the potential vector field Z parallel to the characteristic vector field and with constant scalar curvature then either scalar curvature will vanish or g becomes a δ-Yamabe soliton under a certain condition. We established some results on K-paracontact manifold admitting δ-almost gradient Yamabe soliton. Moreover, we consider a (k, μ)-paracontact metric manifold admitting a non-trivial δ-almost gradient Yamabe soliton. We shown that the potential vector field Z is parallel to ξ. We have also discussed about δ-almost gradient Yamabe soliton on the para-Sasakian manifold. Finally, we consider a para-cosymplectic manifold with a δ-almost Yamabe soliton. In the end, we construct two examples of K-paracontact metric manifolds with δ-almost Yamabe soliton.