Classification of quasi-minimal slant surfaces in Lorentzian complex space forms

Abstract

From J-action point of views, slant surfaces are the simplest and the most natural surfaces of a (Lorentzian) Kahler surface (\( \tilde M,\tilde g \), J). Slant surfaces arise naturally and play some important roles in the studies of surfaces of Kahler surfaces (see, for instance, [13]). In this article, we classify quasi-minimal slant surfaces in the Lorentzian complex plane C12. More precisely, we prove that there exist five large families of quasi-minimal proper slant surfaces in C12. Conversely, quasi-minimal slant surfaces in C12 are either Lagrangian or locally obtained from one of the five families. Moreover, we prove that quasi-minimal slant surfaces in a non-flat Lorentzian complex space form are Lagrangian.