Analysis of a special type of soliton on Kenmotsu manifolds

In this paper, we aim to investigate the properties of an almost *-Ricci-Bourguignon soliton (almost *-R-B-S for short) on a Kenmotsu manifold (K-M). We start by proving that if a Kenmotsu manifold (K-M) obeys an almost *-R-B-S, then the manifold is -Einstein. Furthermore, we establish that if a (, -2) '-nullity distribution, where <-1, has an almost *-Ricci-Bourguignon soliton (almost *-R-B-S), then the manifold is Ricci flat. Moreover, we establish that if a K-M has almost *-Ricci-Bourguignon soliton gradient and the vector field preserves the scalar curvature r, then the manifold is an Einstein manifold with a constant scalar curvature given by r=-n (2n-1). Finaly, we have given en example of a almost *-R-B-S gradient on the Kenmotsu manifold.