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<p>In this paper, <i>k</i>-harmonic submanifolds with parallel mean curvature vector in pseudo-Riemannian space forms are studied. We first investigate the fundamental distinction between biharmonic and <i>k</i>-harmonic submanifolds, proving that any nonminimal biharmonic submanifold with non light-like mean curvature vector in a nonflat pseudo-Riemannian space form can be not <i>k</i>-harmonic (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k\ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>). Then, we give a partial classification of these pseudo-umbilical submanifolds.</p>

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Some Classifications of k-Harmonic Submanifolds in Pseudo-Riemannian Space Forms

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • Li Du,
  • Hongxin Li,
  • Shan Li

摘要

In this paper, k-harmonic submanifolds with parallel mean curvature vector in pseudo-Riemannian space forms are studied. We first investigate the fundamental distinction between biharmonic and k-harmonic submanifolds, proving that any nonminimal biharmonic submanifold with non light-like mean curvature vector in a nonflat pseudo-Riemannian space form can be not k-harmonic ( \(k\ge 3\) k ≥ 3 ). Then, we give a partial classification of these pseudo-umbilical submanifolds.