Some recent progress of biharmonic submanifolds

TL;DR

This paper surveys recent advances in the study of biharmonic submanifolds, including progress on conjectures and classifications, and highlights open problems in the field.

Contribution

It provides a concise overview of recent developments, including progress on key conjectures and classifications in biharmonic submanifold theory.

Findings

Progress on Chen's biharmonic conjecture

Advances in the classification of biharmonic submanifolds of spheres

Identification of open problems in the field

Abstract

In this note, we give a brief survey on some recent developments of biharmonic submanifolds. After reviewing some recent progress on Chen's biharmonic conjecture, the Generalized Chen's conjecture on biharmonic submanifolds of non-positively curved manifolds, and some classifications of biharmonic submanifolds of spheres, we give a short list of some open problems in this topic.