On rigidity results for spacelike $$\xi $$-translator in pseudo-Euclidean spaces $$\mathbb {R}_p^{n+p}$$

Abstract This paper establishes new rigidity theorems for complete spacelike $$\xi $$ -translator immersed in the pseudo-Euclidean space $$\mathbb {R}^{n+p}_p$$ . By imposing suitable upper bounds on the norm $$\Vert \xi \Vert $$ or geometric constraints on the norm of the second fundamental form $$\Vert A\Vert $$ , we apply generalized maximum principles due to Da Silva, Lima Jr. and de Lima (Arch Math 118:663–673, 2022), Chen and Qiu (Adv Math 294:517–531, 2016), and Alias, Caminha and Nascimento (J Math Anal Appl 474: 242–247, 2019). These conditions force the vanishing of the second fundamental form, implying that any such $$\xi $$ -translator is necessarily a spacelike hyperplane of $$\mathbb {R}^{n+p}_p$$ .