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<p>In this paper, we investigate the geometry of compact spacelike biconservative hypersurfaces with constant scalar curvature in de Sitter space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {S}_1^{m+1}(c)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi mathvariant="double-struck">S</mi> <mn>1</mn> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, under some geometric constraints. Moreover, we obtain an additional result by replacing the assumption of constant scalar curvature with an estimate on the dimension of these hypersurfaces. Our results extend the understanding of rigidity properties of such hypersurfaces in pseudo-Riemannian settings.</p>

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Compact spacelike biconservative hypersurfaces in de Sitter space

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Aykut Kayhan

摘要

In this paper, we investigate the geometry of compact spacelike biconservative hypersurfaces with constant scalar curvature in de Sitter space \(\mathbb {S}_1^{m+1}(c)\) S 1 m + 1 ( c ) , under some geometric constraints. Moreover, we obtain an additional result by replacing the assumption of constant scalar curvature with an estimate on the dimension of these hypersurfaces. Our results extend the understanding of rigidity properties of such hypersurfaces in pseudo-Riemannian settings.