Constant $\mu$-scalar curvature K\"ahler metric -- formulation and foundational results
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.
Keywords
Cite
@article{arxiv.1902.00664,
title = {Constant $\mu$-scalar curvature K\"ahler metric -- formulation and foundational results},
author = {Eiji Inoue},
journal= {arXiv preprint arXiv:1902.00664},
year = {2021}
}
Comments
44 pages. v4: Examples are added in section 6. Minor changes. v3: Section 5.2 is added. Chen-Tian formula of $\mu$-Mabuchi functional is corrected (Proposition 4.2). (This change does not affect other results in this article. )