On Riemannian foliations admitting transversal conformal fields

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.

12 pages