Biconservative Hypersurfaces in E14\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {E}^4_1$$\end{document} with Non-diagonalizable Shape Operator

In this paper, we study biconservative isometric immersions into Minkowski 4-space E14\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {E}}_1^4$$\end{document}. We obtain the local classification of biconservative hypersurfaces with non-diagonalizable shape operator. As a result, we complete the local study of biconservative hypersurfaces of E14\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {E}}_1^4$$\end{document} initiated in Fu and Turgay (Int J Math 27:1650041, 2016). We also get some results considering the intrinsic properties of this class of hypersurfaces.