In this paper, we consider biconservative and biharmonic isometric immersions into the 4-dimensional Lorentzian space form \({\mathbb {L}}^4(\delta )\) with constant sectional curvature \(\delta \). We obtain some local classifications of biconservative CMC surfaces in \({\mathbb {L}}^4(\delta )\). Further, we get complete classification of biharmonic CMC surfaces in the de Sitter 4-space. We also proved that there is no biharmonic CMC surface in the anti-de Sitter 4-space. Further, we get the classification of biconservative, quasi-minimal surfaces in Minkowski-4 space.

中文翻译：

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洛伦兹空间形式中具有恒定平均曲率的双保守曲面

在本文中，我们考虑双保守和双调和等距浸入到具有恒定截面曲率\(\delta \) 的 4 维洛伦兹空间形式\({\mathbb {L}}^4(\delta )\)中。我们在\({\mathbb {L}}^4(\delta )\)中获得了双保守 CMC 曲面的一些局部分类。此外，我们得到了 de Sitter 4 空间中双调和 CMC 曲面的完整分类。我们还证明了反德西特4空间中不存在双调和CMC面。此外，我们得到了 Minkowski-4 空间中双保守、拟极小曲面的分类。