Explicit classification of biconservative surfaces in Lorentz 3-space forms

Abstract

Biconservative submanifolds are defined as conservative stress–energy tensor with respect to the bienergy, which is a natural generalization of biharmonic submanifolds. R. Caddeo et al. classified biconservative surfaces in 3-dimensional Riemannian space forms. In this article, we give a complete explicit classification of biconservative surfaces in de Sitter 3-spaces and anti-de Sitter 3-spaces.