A short survey on biharmonic Riemannian submersions

TL;DR

This paper provides a concise survey of biharmonic Riemannian submersions, highlighting recent progress and their relation to biharmonic submanifolds over the past three decades.

Contribution

It offers a summarized overview of the development and key results in the study of biharmonic Riemannian submersions, a dual concept to biharmonic submanifolds.

Findings

Summarizes recent advances in biharmonic Riemannian submersions

Highlights the duality with biharmonic submanifolds

Provides a foundation for future research in the area

Abstract

The study of biharmonic submanifolds, initiated by B. Y. Chen and G. Y. Jiang independently, has received a great attention in the past 30 years with many important progress. This note attempts to give a short survey on the study of biharmonic Riemannian submersions which are a dual concept of biharmonic submanifolds (i.e., biharmonic isometric immersions).