Biharmonic surfaces with parallel mean curvature in complex space forms

TL;DR

This paper classifies complete biharmonic surfaces with parallel mean curvature vectors in complex space forms, focusing on those with non-negative Gaussian curvature, advancing understanding of their geometric properties.

Contribution

It provides a classification of such surfaces, a novel result in the study of biharmonic submanifolds in complex space forms.

Findings

Complete biharmonic surfaces with parallel mean curvature are classified.

Surfaces with non-negative Gaussian curvature are characterized.

New geometric properties of these surfaces are identified.

Abstract

We classify complete biharmonic surfaces with parallel mean curvature vector field and non-negative Gaussian curvature in complex space forms.