On conformal submersions with geodesic or minimal fibers

Abstract

We prove that every conformal submersion from a round sphere onto an Einstein manifold with fbers being geodesics is—up to an isometry—the Hopf fbration composed with a conformal difeomorphism of the complex projective space of appropriate dimension. We also show that there are no conformal submersions with minimal fbers between manifolds satisfying certain curvature assumptions.