Lorentz hypersurfaces \(M_{1}^{4}\) is studied in \(E_{1}^{5}\) with non-diagonal shape operators having characteristic equation \((y-\lambda )^2(y-\lambda _3)(y-\lambda _4)\) or \((y-\lambda )^3(y-\lambda _4)\) or \(((y-\lambda )^2+\mu ^2)(y-\lambda _3)(y-\lambda _4)\). It is proved that if the mean curvature vector field \(\vec {H}\) of Lorentz hypersurfaces \(M_{1}^{4}\) in \(E_{1}^{5}\) with non-diagonal shape operators satisfies the equation \(\triangle \vec {H}= \alpha \vec {H}\) (for a constant \(\alpha \)), then \(M_{1}^{4}\) has constant mean curvature.

中文翻译：

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伪欧几里得空间中的洛伦兹超曲面$$ E_ {1} ^ {5} $$ E15

使用具有特征方程\（（y- \ lambda）^ 2（y ）的非对角形状算子在\（E_ {1} ^ {5} \）中研究Lorentz超曲面\（M_ {1} ^ {4} \）-\ lambda _3）（y- \ lambda _4）\）或\（（y- \ lambda）^ 3（y- \ lambda _4）\）或\（（（y- \ lambda ^^ 2 + \ mu ^ 2）（y- \ lambda _3）（y- \ lambda _4）\）。证明如果Lorentz超曲面\（M_ {1} ^ {4} \）中的Lorentz超曲面\（E_ {1} ^ {5} \）的平均曲率矢量场\（\ vec {H } \）具有非对角线形状运算符满足方程\（\ triangle \ vec {H} = \ alpha \ vec {H} \）（对于常数\（\ alpha \）），然后满足\（M_ {1} ^ {4} \） 具有恒定的平均曲率。