2018/08/16 by Changliang Wang, Y. K. Wang, Wang, Changliang +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.1808.05679
23 pages
openalex publication_date 2018/08/16 · arxiv created 2018/10/10 · arxiv updated 2018/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the linear stability of Einstein metrics of Riemannian submersion type. First, we derive a general instability condition for such Einstein metrics and provide some applications. Then we study instability arising from Riemannian product structures on the base. As an application, we estimate the coindex of the Einstein metrics constructed in \citeWZ90 and \citeWan92. Finally, we investigate more closely the linear stability of Einstein metrics from circle bundle constructions and obtain a rigidity result for linearly stable Einstein metrics of this type.