Biconservative quasi-minimal immersions into semi-Euclidean spaces

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, where $c\in\{0,-1,1\}$. 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 isometric immersion into $\mathbb E^4_2$.