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

Abstract

In this paper, we study biconservative immersions into the semi-Riemannian space form R24(c) of dimension 4, index 2 and constant curvature c is an element of {0,-1,1}. First, we obtain a characterization of quasi-minimal proper biconservative immersions into R24(c). Then we obtain the complete classification of quasi-minimal biconservative surfaces in R24(0)=E24. We also obtain a new class of biharmonic quasi-minimal surfaces in E24.