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<p>This paper studies biharmonic hypersurfaces with constant-norm second fundamental form in non-flat pseudo-Riemannian space forms <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N_q^6(c)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>N</mi> <mi>q</mi> <mn>6</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Under the assumptions that the shape operator is diagonalizable and has at most four distinct principal curvatures, we prove that such a hypersurface must have constant mean curvature and constant scalar curvature.</p>

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On biharmonic hypersurfaces in 6-dimensional pseudo-Riemannian space forms

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • Li Du,
  • Hongxin Li,
  • Shan Li

摘要

This paper studies biharmonic hypersurfaces with constant-norm second fundamental form in non-flat pseudo-Riemannian space forms \(N_q^6(c)\) N q 6 ( c ) . Under the assumptions that the shape operator is diagonalizable and has at most four distinct principal curvatures, we prove that such a hypersurface must have constant mean curvature and constant scalar curvature.