On Riemannian foliations admitting transversal conformal fields

TL;DR

This paper investigates conditions under which a Riemannian foliation with constant transversal scalar curvature admits transversal conformal fields, leading to the foliation being transversally isometric to a sphere.

Contribution

It generalizes conditions for Riemannian foliations to be transversally spherical when admitting transversal conformal fields.

Findings

Foliation is transversally isometric to a sphere under certain conditions.

Identifies generalized conditions for the existence of transversal conformal fields.

Provides criteria linking transversal conformal fields to spherical geometry.

Abstract

Let $(M,g_M,\mathcal F)$ be a closed, connected Riemannian manifold with a Riemannian foliation $\mathcal F$ of nonzero constant transversal scalar curvature. When $M$ admits a transversal nonisometric conformal field, we find some generalized conditions that $\mathcal F$ is transversally isometric to the sphere.