In this paper, we study biconservative immersions into the semi-Riemannian space form \(R^4_2(c)\) of dimension 4, index 2 and constant curvature \(c\in \{0,-1,1\}\). First, we obtain a characterization of quasi-minimal proper biconservative immersions into \(R^4_2(c)\). Then we obtain the complete classification of quasi-minimal biconservative surfaces in \(R^4_2(0)={\mathbb {E}}^4_2\). We also obtain a new class of biharmonic quasi-minimal surfaces in \({\mathbb {E}}^4_2\).

中文翻译：

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关于半欧半空间中的守恒拟最小浸入

在本文中，我们研究了双保守浸入尺寸为4，索引为2且等曲率\（c \ in \ {0，-1,1 \} \\}的半黎曼空间形式\（R ^ 4_2（c）\））。首先，我们获得了对\（R ^ 4_2（c）\）的拟最小适当双保守沉浸的表征。然后我们获得\（R ^ 4_2（0）= {\ mathbb {E}} ^ 4_2 \）中的准最小双保守曲面的完整分类。我们还在\（{\ mathbb {E}} ^ 4_2 \）中获得了一类新的双调和准最小曲面。