Mabuchi's soliton metric and relative D-stability

2019/05/15 by Tomoyuki Hisamoto, Hisamoto, Tomoyuki · 1 citation
Mathematics · #32Q20 #32Q26 #53C44 #53C55 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #math.DG #msc:32Q20 #msc:32Q26 #msc:53C44 #msc:53C55

paper · pdf · doi:10.48550/arxiv.1905.05948

We fixed the proof of the main theorem in the first version, following the work of Professor C. Li

openalex publication_date 2019/05/15 · arxiv created 2020/01/10 · arxiv updated 2020/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For Fano manifolds T. Mabuchi introduced a generalization of the Kähler-Einstein metric, which is characterized as the critical point of the Ricci-Calabi functional. We show that a Fano manifold admits Mabuchi's metric if and only if it is uniformly relatively D-stable.

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