Introduction to gradient h-almost η-Ricci soliton warped product

Abstract

In this paper, we introduce the new concept of gradient h-almost η-Ricci soliton. We discuss here a steady or expanding gradient h-almost η-Ricci soliton warped product Bn ×f Fm, m > 1. We show that the warping function f of this warped product attains minimum as well as maximum and it will definitely be a Riemannian product under certain conditions. We also describe some suitable restrictions to these constructions for the compact base of this warped product. Later, we study h-almost η-Ricci soliton and gradient h-almost η-Ricci soliton on warped product manifolds including a concurrent vector field.