Quasi-biharmonic Lagrangian surfaces in Lorentzian complex space forms

TL;DR

This paper introduces the concept of quasi-biharmonic submanifolds in pseudo-Riemannian manifolds and classifies specific Lagrangian surfaces in Lorentzian complex space forms, expanding understanding of their geometric properties.

Contribution

It defines quasi-biharmonic submanifolds in pseudo-Riemannian manifolds and provides a classification of quasi-biharmonic marginally trapped Lagrangian surfaces in Lorentzian complex space forms.

Findings

Classification of quasi-biharmonic marginally trapped Lagrangian surfaces.

Introduction of the notion of quasi-biharmonic submanifolds in pseudo-Riemannian geometry.

Extension of biharmonic theory to Lorentzian complex space forms.

Abstract

In this paper, we introduce the notion of a quasi-biharmonic submanifold in a pseudo-Riemannian manifold and classify quasi-biharmonic marginally trapped Lagrangian surfaces in Lorentzian complex space forms.