Biharmonic Pseudo-Riemannian submersions from 3-manifolds

TL;DR

This paper classifies pseudo-Riemannian biharmonic submersions from 3D space forms to surfaces, advancing understanding of biharmonic maps in pseudo-Riemannian geometry.

Contribution

It provides a complete classification of biharmonic submersions from 3-manifolds into surfaces in the pseudo-Riemannian setting.

Findings

Classification of biharmonic submersions achieved

Identifies conditions for biharmonicity in pseudo-Riemannian submersions

Extends biharmonic theory to pseudo-Riemannian manifolds

Abstract

We classify the pseudo-Riemannian biharmonic submersion from a 3-dimensional space form into a surface.