Biharmonic Riemannian maps

TL;DR

This paper establishes conditions for Riemannian maps to be biharmonic and introduces pseudo-umbilical Riemannian maps, revealing their impact on the geometry of base manifolds.

Contribution

It provides necessary and sufficient conditions for biharmonic Riemannian maps and defines pseudo-umbilical Riemannian maps as a new generalization.

Findings

Characterization of biharmonic Riemannian maps

Introduction of pseudo-umbilical Riemannian maps

Restrictions on base manifolds due to pseudo-umbilical maps

Abstract

We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that such Riemannian maps put some restrictions on the base manifolds.