On transversally harmonic maps of foliated Riemannian manifolds

TL;DR

This paper investigates transversally harmonic maps between foliated Riemannian manifolds, demonstrating that under certain curvature conditions, these maps are necessarily transversally totally geodesic, thus revealing geometric constraints.

Contribution

The paper establishes a new curvature condition under which transversally harmonic maps are transversally totally geodesic, advancing understanding of foliated Riemannian geometry.

Findings

Transversally harmonic maps are transversally totally geodesic under specific curvature conditions.

Curvature conditions influence the geometric behavior of harmonic maps in foliated manifolds.

The results provide new insights into the structure of foliated Riemannian manifolds.

Abstract

We study the transversally harmonic maps between foliated Riemannian manifolds. In particular, we prove that under some curvature conditions, any transversally harmonic map is transversally totally geodesic.