Liouville type theorems for transversally harmonic and biharmonic maps

TL;DR

This paper investigates Liouville theorems for transversally harmonic and biharmonic maps within the context of foliated Riemannian manifolds, aiming to understand conditions under which such maps are trivial.

Contribution

It provides new Liouville theorems specifically for transversally harmonic and biharmonic maps on foliated Riemannian manifolds, expanding the theoretical understanding of these maps.

Findings

Liouville theorems established for transversally harmonic maps

Liouville theorems established for transversally biharmonic maps

Conditions under which these maps are trivial are identified

Abstract

We study the Liouville type theorems for transversally harmonic and biharmonic maps on foliated Riemannian manifolds