Riemannian foliations admitting transversal conformal fields II

Abstract

Let \((M,g_M,{\mathcal {F}})\) be a closed, oriented Riemannian manifold with a foliation \({\mathcal {F}}\) of codimension \(q\) and a bundle-like metric \(g_M\). Assume that the transversal scalar curvature is non-zero constant. If \(M\) admits a transversal conformal field satisfying some conditions, then \({\mathcal {F}}\) is transversally isometric to a sphere.