CLASSIFICATION OF PSEUDO-UMBILICAL SLANT SURFACES IN LORENTZIAN COMPLEX SPACE FORMS

Abstract

In this paper we prove that slant surfaces in a non-flat Lorentzian complex space form must be Lagrangian. By applying this result, we completely classify pseudo-umbilical slant surfaces in Lorentzian complex space forms. Our classification results state that there exist two families of pseudo-umbilical slant surfaces in Lorentzian complex plane $\mathbb{C}^2_1$, three families in complex projective plane $CP^2_1$, and three families in complex hyperbolic plane $CH^2_1$.