Geometric classifications of k-almost Ricci solitons admitting paracontact metrices

The prime objective of the approach is to give geometric classifications of k-almost Ricci solitons associated with paracontact manifolds. Let M2n+1 (f, ?, ?, g ) be a paracontact metric manifold, and if a K-para-contact metric g represents a k-almost Ricci soliton (g, V, k, ?) and the potential vector field V is Jacobi field along the Reeb vector field ?, then either k = ? - 2n, or g is a k-Ricci soliton. Next, we consider K-paracontact manifold as a k-almost Ricci soliton with the potential vector field V is infinitesimal paracontact transformation or collinear with ?. We have proved that if a paracontact metric as a k-almost Ricci soliton associated with the non-zero potential vector field V is collinear with ? and the Ricci operator Q commutes with paracontact structure f, then it is Einstein of constant scalar curvature equals to -2 n(2 n + 1). Finally, we have deduced that a para-Sasakian manifold admitting a gradient k-almost Ricci soliton is Einstein of constant scalar curvature equals to -2 n(2 n + 1).

Automated summary

This article investigates the geometric classification and properties of k-almost Ricci solitons associated with paracontact manifolds, and derives some conclusions.