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<p>In this paper, we prove that two classes of biconservative hypersurfaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(M^3_r\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>M</mi> <mi>r</mi> <mn>3</mn> </msubsup> </math></EquationSource> </InlineEquation> with constant scalar curvature in a 4-dimensional pseudo-Riemannian space form must have constant mean curvature: (i) those with general index <i>r</i> and diagonalizable shape operator; (ii) the Lorentz ones, that is <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(r=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, without any restrictions.</p>

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Rigidity of Biconservative Hypersurfaces in 4-Dimensional Pseudo-Riemannian Space Forms

  • 期刊论文

  • 发表日期：

    2026年5月23日

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  • Li Du

摘要

In this paper, we prove that two classes of biconservative hypersurfaces \(M^3_r\) M r 3 with constant scalar curvature in a 4-dimensional pseudo-Riemannian space form must have constant mean curvature: (i) those with general index r and diagonalizable shape operator; (ii) the Lorentz ones, that is \(r=1\) r = 1 , without any restrictions.