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<p>This paper establishes new rigidity theorems for complete spacelike <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\xi \)</EquationSource> </InlineEquation>-translator immersed in the pseudo-Euclidean space <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\mathbb {R}^{n+p}_p\)</EquationSource> </InlineEquation>. By imposing suitable upper bounds on the norm <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\Vert \xi \Vert \)</EquationSource> </InlineEquation> or geometric constraints on the norm of the second fundamental form <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\Vert A\Vert \)</EquationSource> </InlineEquation>, 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 <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\xi \)</EquationSource> </InlineEquation>-translator is necessarily a spacelike hyperplane of <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\mathbb {R}^{n+p}_p\)</EquationSource> </InlineEquation>.</p>

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

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  • 发表日期：

    2026年3月26日

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  • Weiller F. Chaves Barboza

摘要

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 \(\mathbb {R}^{n+p}_p\) .