Classification of Lorentz surfaces with parallel mean curvature vector in non-flat pseudo-Riemannian space forms $S_2^4(1)$ and $H_2^4(-1)$

Abstract

Lorentz surfaces with parallel mean curvature vector in $\mathbb{E}_2^4$ have been classified in [14]. In this paper, we continue to classify Lorentz surfaces with parallel mean curvature vector in pseudo-Riemannian space forms $S_2^4(1)$ and $H_2^4(-1)$. Consequently, we achieve the complete classification of Lorentz surfaces with parallel mean curvature vector in 4-dimensional neutral indefinite space form with index 2.