Metrics of constant scalar curvature on sphere bundles

Abstract

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

22 pages

References in corpus (3)

• Symmetry and Asymmetry: The Method of Moving Spheres
• Multiplicity of solutions to the Yamabe problem on collapsing Riemannian submersions
• Constant scalar curvature metrics on Hirzebruch surfaces

Cited by in corpus (2)

• Global bifurcation for a class of nonlinear ODEs
• Multiplicity of constant scalar curvature metrics on warped products