Kayhan, A.Turgay, Nurettin Cenk2024-07-122024-07-1220240025-58581865-878410.1007/s12188-023-00273-x2-s2.0-85183435837https://doi.org/10.1007/s12188-023-00273-xhttps://hdl.handle.net/20.500.12415/7270In this paper, we consider biconservative and biharmonic isometric immersions into the 4-dimensional Lorentzian space form L4(delta)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {L}}<^>4(\delta )$$\end{document} with constant sectional curvature delta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}. We obtain some local classifications of biconservative CMC surfaces in L4(delta)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {L}}<^>4(\delta )$$\end{document}. 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.eninfo:eu-repo/semantics/closedAccessBiconservative SurfacesConstant Mean CurvatureLorentzian Space FormsQuasi-Minimal SurfacesDe Sitter SpaceArticleQ4WOS:001150779700001N/A