Positive Einstein Metrics with \mathbbS^4m+3 as Principal Orbit

2022/10/24 by Hanci Chi, Chi, Hanci
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2210.13216

openalex publication_date 2022/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that there exists at least one positive Einstein metric on \mathbbHP^m+1\sharp \mathbbHP^m+1 for m≥ 2. Based on the existence of the first Einstein metric, we give a criterion to check the existence of a second Einstein metric on \mathbbHP^m+1\sharp \mathbbHP^m+1. We also investigate the existence of cohomogeneity one positive Einstein metrics on \mathbbS^4m+4 and prove the existence of a non-standard Einstein metric on \mathbbS⁸.

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