The geometry of 2-Killing vector fields in sequential doubly warped products

Abstract We establish a new type of warped products named sequential doubly warped products and investigate the relationship between the properties of Killing or 2-Killing of a vector field on these manifolds and its components on the individual factor manifolds. Our results demonstrate that a Ricci soliton factor manifold, influenced by a Killing vector field on the sequential doubly warped product, is an Einstein manifold if and only if it satisfies certain conditions. Additionally, we show that under specific conditions, the factor manifold associated with Euclidean space is isometric if a portion of the Killing vector field is of gradient type. Furthermore, we establish the necessary and sufficient conditions for reducing a sequential doubly warped product to a doubly warped product (DWP) and a direct product. Lastly, we characterize the 2-Killing vector fields in sequential doubly warped spacetimes, using the static standard spacetime as an illustrative example.