Metrics of constant scalar curvature on sphere bundles

Let G/HG/H be a Riemannian homogeneous space. For an orthogonal representation ϕ of H   on the Euclidean space Rk+1Rk+1, there corresponds the vector bundle E=G×ϕRk+1→G/HE=G×ϕRk+1→G/H with fiberwise inner product. Provided that ϕ is the direct sum of at most two representations which are either trivial or irreducible, we construct metrics of constant scalar curvature on the unit sphere bundle UE of E  . When G/HG/H is the round sphere, we study the number of constant scalar curvature metrics in the conformal classes of these metrics.