ON QUASI-MINIMAL ISOMETRIC IMMERSIONS INTO NON-FLAT SEMI RIEMANNIAN SPACE FORMS OF INDEX TWO

Abstract

In this paper, first we gave a summary of recent results on biconservative immersions. Then, we obtained a necessary and sufficient condition for the existence of biconservative quasi-minimal immersions into a four dimensional semi-Riemannian space form of index two with non-zero sectional curvatures. We also constructed an explicit example of biconservative quasi-minimal surface.