On rigidity results for spacelike ξ-translator in pseudo-Euclidean spaces Rₚⁿ⁺ᵖ

This paper establishes new rigidity theorems for complete spacelike ξ -translator immersed in the pseudo-Euclidean space Rⁿ⁺ᵖₚ . By imposing suitable upper bounds on the norm ξ or geometric constraints on the norm of the second fundamental form A , 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 ξ -translator is necessarily a spacelike hyperplane of Rⁿ⁺ᵖₚ .