Abstract
Let G/H be a Riemannian homogeneous space. For an orthogonal representation ϕ of H on the Euclidean space Rk+1, there corresponds the vector bundle E=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/H is the round sphere, we study the number of constant scalar curvature metrics in the conformal classes of these metrics.
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