Almost Riemann solitons and gradient almost Riemann solitons on Lp-Sasakian manifolds

Abstract

The upcoming article aims to investigate almost Riemann solitons and gradient almost Riemann solitons in a LP-Sasakian manifoldM3. At first, it is proved that if (1,Z,?) be an almost Riemann soliton on a LP-Sasakian manifold M3, then it reduces to a Riemann soliton, provided the soliton vector Z has constant divergence. Also, we show that if Z is pointwise collinear with the characteristic vector field ?, then Z is a constant multiple of ?, and the ARS reduces to a Riemann soliton. Furthermore, it is proved that if a LP-Sasakian manifold M3 admits gradient almost Riemann soliton, then the manifold is a space form. Also, we consider a non-trivial example and validate a result of our paper.