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


Krishnendu De




The upcoming article aims to investigate almost Riemann solitons and gradient almost Riemann solitons in a LP-Sasakian manifold M 3. At first, it is proved that if (, Z, λ) be an almost Riemann soliton on a LP-Sasakian manifold M 3 , 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 ξ, then Z is a constant multiple of ξ, and the ARS reduces to a Riemann soliton. Furthermore, it is proved that if a LP-Sasakian manifold M 3 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