Conformal product structures on compact manifolds with constant sectional curvature

2026/05/31 by Xianfeng Jiang
Mathematics · #math.DG

paper · pdf

arxiv created 2026/08/02 · arxiv updated 2026/08/04

Abstract

We prove that compact non-flat manifolds of constant sectional curvature admit no conformal product structure. In the flat case, we show that in dimensions at least three every conformal product structure is trivial, namely its Weyl connection is the Levi-Civita connection of the given flat metric; flat surfaces are exceptional. Furthermore, we demonstrate that the methods extend naturally to irreducible, compact locally symmetric spaces of non-positive curvature.

Citations

• Reducible Riemannian manifolds with conformal product structures
• Conformal product structures on compact Einstein manifolds
• Conformal product structures on compact Kähler manifolds
• The structure of locally conformally product Lie algebras
• The characteristic group of locally conformally product structures