  Let $G/H$ be a Riemannian homogeneous space. For an orthogonal representation
$\phi$ of $H$ on the Euclidean space $\mathbb{R}^{k+1}$, there corresponds the
vector bundle $E=G\times_{\phi}\mathbb{R}^{k+1} \to G/H$ with fiberwise inner
product. Provided that $\phi$ 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.
