The Dirichlet Problem for Einstein Metrics on Cohomogeneity One\n Manifolds

2017/10/05 by Timothy Buttsworth, Buttsworth, Timothy
Mathematics · Physics and Astronomy · #53C20 #53C30 #58J32 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1710.02037

openalex publication_date 2017/10/05 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

Let G/H be a compact homogeneous space, and let \g₀ and \g₁\nbe G-invariant Riemannian metrics on G/H. We consider the problem of\nfinding a G-invariant Einstein metric g on the manifold G/H\× [0,1]\nsubject to the constraint that g restricted to G/H\× 0 and\nG/H\× 1 coincides with \g₀ and \g₁, respectively. By\nassuming that the isotropy representation of G/H consists of pairwise\ninequivalent irreducible summands, we show that we can always find such an\nEinstein metric.\n

Related

• Cohomogeneity-One Quasi-Einstein Metrics
• Non-existence of cohomogeneity one Einstein metrics of two summands
• Existence of cohomogeneity one Einstein metrics
• Counting Homogeneous Einstein Metrics
• Cohomogeneity one Kahler and Kahler-Einstein manifolds with one singular orbit, I