Null pseudo-isotropic Lagrangian surfaces

TL;DR

This paper characterizes null pseudo-isotropic Lagrangian Lorentzian surfaces in complex pseudo space forms, showing they are minimal, and classifies those that are lightlike pseudo-isotropic but not pseudo-isotropic.

Contribution

It provides a complete characterization and classification of null pseudo-isotropic Lagrangian Lorentzian surfaces in complex pseudo space forms.

Findings

Null pseudo-isotropic Lagrangian Lorentzian surfaces are minimal.

Classification of lightlike pseudo-isotropic but not pseudo-isotropic surfaces.

Characterization of pseudo-isotropic condition in Lorentzian surfaces.

Abstract

In this paper we will show that a Lagrangian, Lorentzian surface $M^2_1$ in a complex pseudo space form $\widetilde M^2_1 (4c)$ is pseudo-isotropic if and only if $M$ is minimal. Next we will obtain a complete classification of all Lagrangian, Lorentzian surfaces which are lightlike pseudo-isotropic but not pseudo-isotropic.