Metrics of constant scalar curvature on sphere bundles

2015/06/30 by Nobuhiko Otoba, Jimmy Petean
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Combinatorics #Conformal map #Constant (computer programming) #Constant curvature #Curvature #Euclidean space #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #Scalar (mathematics) #Scalar curvature #Vector bundle #math.DG #msc:53C20

paper · pdf · doi:10.1016/j.difgeo.2016.02.007

published as Differential Geom. Appl. Volume 46, June 2016, Pages 146--163 · 22 pages

openalex publication_date 2016/03/05 · arxiv created 2016/03/08 · arxiv updated 2016/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Let G/H be a Riemannian homogeneous space. For an orthogonal representation ϕ of H on the Euclidean space ℝ^k+1, there corresponds the vector bundle E=G×_ϕℝ^k+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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