<p>In this paper, we study a biconservative hypersurface <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$M^4_r$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>M</mi> <mi>r</mi> <mn>4</mn> </msubsup> </math></EquationSource> </InlineEquation> with constant scalar curvature <i>R</i> in the pseudo-Riemannian space form <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$N^5_q(c)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>N</mi> <mi>q</mi> <mn>5</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, and show that if <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$M^4_r$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>M</mi> <mi>r</mi> <mn>4</mn> </msubsup> </math></EquationSource> </InlineEquation> has diagonalizable shape operator, then it is either cmc or a non-cmc one with two distinct principal curvatures <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\lambda _2=\lambda _3=\lambda _4=-\lambda _1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>λ</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>λ</mi> <mn>4</mn> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$R=12c$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mo>=</mo> <mn>12</mn> <mi>c</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

On Biconservative Hypersurfaces with Constant Scalar Curvature in Pseudo-Riemannian Space Forms

期刊论文
发表日期：

2026年4月15日

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Li Du,
Tian Nie

摘要

In this paper, we study a biconservative hypersurface $M^4_r$ $M_{r}^{4}$ with constant scalar curvature R in the pseudo-Riemannian space form $N^5_q(c)$ $N_{q}^{5} (c)$ , and show that if $M^4_r$ $M_{r}^{4}$ has diagonalizable shape operator, then it is either cmc or a non-cmc one with two distinct principal curvatures $\lambda _2=\lambda _3=\lambda _4=-\lambda _1$ $λ_{2} = λ_{3} = λ_{4} = - λ_{1}$ and $R=12c$ $R = 12 c$ .