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<p>In this paper, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>-biconservative PNMC submanifolds <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(M^m_r\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>M</mi> <mi>r</mi> <mi>m</mi> </msubsup> </math></EquationSource> </InlineEquation> with diagonalizable shape operator and at most two principal curvatures in the direction of the mean curvature vector field in pseudo-Riemannian space forms are studied. We prove that such submanifolds have parallel mean curvature vector field provided that the scalar curvature of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(M^m_r\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>M</mi> <mi>r</mi> <mi>m</mi> </msubsup> </math></EquationSource> </InlineEquation> is a constant.</p>

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On \(\varvec{\lambda }\)-biconservative submanifolds in pseudo-Riemannian space forms

  • 期刊论文

  • 发表日期：

    2025年8月23日

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  • Li Du,
  • Shan Li,
  • Tian Nie

摘要

In this paper, \(\lambda \) λ -biconservative PNMC submanifolds \(M^m_r\) M r m with diagonalizable shape operator and at most two principal curvatures in the direction of the mean curvature vector field in pseudo-Riemannian space forms are studied. We prove that such submanifolds have parallel mean curvature vector field provided that the scalar curvature of \(M^m_r\) M r m is a constant.