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

From J-action point of views, slant surfaces are the simplest and the most natural surfaces of a (Lorentzian) Kähler surface (\(\tilde M,\tilde g\), J). Slant surfaces arise naturally and play some important roles in the studies of surfaces of Kähler surfaces (see, for instance, 13]). In this article, we classify quasi-minimal slant surfaces in the Lorentzian complex plane C ₁ ² . More precisely, we prove that there exist five large families of quasi-minimal proper slant surfaces in C ₁ ² . Conversely, quasi-minimal slant surfaces in C ₁ ² 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.