On Riemannian foliations admitting transversal conformal fields

Abstract

Let $(M,g_M, \mathscr F)$ be a closed, connected Riemannian manifold with a Riemannian foliation $\mathscr F$ of nonzero constant transversal scalar curvature. When $M$ admits a transversal nonisometric conformal field, we find some generalized conditions that $\mathscr F$ is transversally isometric to $(S^q(1/c),G)$, where $G$ is the discrete subgroup of $O(q)$ acting by isometries on the last $q$ coordinates of the sphere $S^q(1/c)$ of radius $1/c$.