On biharmonic surfaces in pseudo-Riemannian 4-dimensional space forms

Abstract

In this paper, biharmonic pseudo-Riemannian surfaces with diagonalizable shape operetor in pseudo-Riemannian space form \(N_8^4 (c)\) are studied. We prove that the surfaces with light-like mean curvature vector field are pseudo-umbilical. For non light-like mean curvature vector field, we show that the pseudo-umbilical surfaces is minimal or \( H^2 = |c| \). Also, we give some sufficient conditions for such surfaces with parallel mean curvature vector field to be minimal.