2017/12/21 by Yan Li, Li, Yan, Xiaohua Zhu +1
Mathematics · Physics and Astronomy · #53C25 (Primary) #53C55 #58J05 (Secondary) #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.1712.07934
openalex publication_date 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a class of Sasaki manifolds with a reductive G-group action, called G-Sasaki manifolds. By reducing K-energy to a functional defined on a class of convex functions on a moment polytope, we give a criterion for the properness of K-energy. In particular, we deduce a sufficient and necessary condition related to the polytope for the existence of transverse G-Sasaki Einstein metrics. A similar result is also obtained for transverse G-Sasaki Ricci solitons. As an application, we construct several examples of G-Sasaki Ricci solitons by an established openness theorem for transverse G-Sasaki Ricci solitons.