Constant μ-scalar curvature Kähler metric -- formulation and foundational results

2019/02/02 by Inoue, Eiji
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.00664

Abstract

We introduce mu-scalar curvature for a K"ahler metric with a moment map mu and start up a study on constant mu-scalar curvature K"ahler metric as a generalization of both cscK metric and K"ahler-Ricci soliton and as a continuity path to extremal metric. We study some fundamental constraints to the existence of constant mu-scalar curvature K"ahler metric by investigating a volume functional as a generalization of Tian-Zhu's work, which is closely related to Perelman's W-functional. A new K-energy is studied as an approach to the uniqueness problem of constant mu-scalar curvature and as a prelude to new K-stability concept.

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