2-Killing vector fields on multiply warped product manifolds

We characterize 2-Killing vector fields on multiply warped product manifolds. We find the necessary and sufficient conditions for the lift of a vector field on a factor manifold (M-t, r(t)), t = (1,n) over bar, to be a 2-Killing vector field on the multiply warped product manifold, providing also conditions for the component of a Killing or a 2-Killing vector field on a multiply warped product to be a 2-Killing vector field on a factor manifold. Moreover, under certain assumptions, we prove that the component of a Killing or a 2-Killing vector field on a multiply warped product manifold is the potential vector field of a Ricci or a hyperbolic Ricci soliton factor manifold, respectively. As physical applications, we consider the spacetime case, constructing examples of 2-Killing vector fields on the generalized Robertson-Walker and on the generalized Kasner spacetimes.