Nonexistence and rigidity of spacelike mean curvature flow solitons immersed in a GRW spacetime

We study the nonexistence and rigidity of an important class of particular cases of trapped submanifolds, more precisely, n -dimensional spacelike mean curvature flow solitons related to the closed conformal timelike vector field 𝒦=f(t)∂ _t ( t∈ I⊂ℝ ) which is globally defined on an (n+p+1) -dimensional generalized Robertson–Walker (GRW) spacetime -I× _fM^n+p with warping function f∈ C^∞ (I) and Riemannian fiber M^n+p , via applications of suitable generalized maximum principles and under certain constraints on f and on the curvatures of M^n+p . In codimension 1, we also obtain new Calabi–Bernstein-type results concerning the spacelike mean curvature flow soliton equation in a GRW spacetime.