What question did this study set out to answer?

The study aims to establish new rigidity results for complete spacelike xi-translators in pseudo-Euclidean spaces.

March 28, 2026Open Access

On rigidity results for spacelike -translator in pseudo-Euclidean spaces Rₚ^n+p

Key Points

The study aims to establish new rigidity results for complete spacelike xi-translators in pseudo-Euclidean spaces.
Introduced upper bounds on the norm of xi
Applied geometric constraints on the second fundamental form
Utilized generalized maximum principles from previous research
Showed that condition on norms leads to the vanishing of the second fundamental form
Concluded that xi-translators are spacelike hyperplanes in pseudo-Euclidean spaces

Abstract

Abstract This paper establishes new rigidity theorems for complete spacelike -translator immersed in the pseudo-Euclidean space R^n+pₚ. By imposing suitable upper bounds on the norm 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 -translator is necessarily a spacelike hyperplane of R^n+pₚ.

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