On the Biconservative Quasi-Minimal Immersions into Semi-Euclidean Spaces

Abstract

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 $${\mathbb {E}}^4_2$$ .