Mabuchi solitons and Mabuchi constants on Fano admissible manifolds

Fuente: arXiv
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Main Authors: Murayama, Shotaro, Nitta, Yasufumi
Format: Preprint
Published: 2026
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author Murayama, Shotaro
Nitta, Yasufumi
author_facet Murayama, Shotaro
Nitta, Yasufumi
contents In this paper, we study the existence of Mabuchi solitons on admissible manifolds as defined by Apostolov--Calderbank--Gauduchon--Tønnesen-Friedman. We prove that a Fano admissible manifold admits a Mabuchi soliton if and only if the Mabuchi constant is less than 1. We also provide an explicit formula for the Mabuchi constant on Fano admissible manifolds, which generalizes that of Mabuchi. Using this formula, we completely determine the existence and non-existence of Mabuchi solitons on Fano admissible manifolds over the complex projective space $\mathbf{P}^{n}$.
format Preprint
id arxiv_https___arxiv_org_abs_2604_23261
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Mabuchi solitons and Mabuchi constants on Fano admissible manifolds
Murayama, Shotaro
Nitta, Yasufumi
Differential Geometry
In this paper, we study the existence of Mabuchi solitons on admissible manifolds as defined by Apostolov--Calderbank--Gauduchon--Tønnesen-Friedman. We prove that a Fano admissible manifold admits a Mabuchi soliton if and only if the Mabuchi constant is less than 1. We also provide an explicit formula for the Mabuchi constant on Fano admissible manifolds, which generalizes that of Mabuchi. Using this formula, we completely determine the existence and non-existence of Mabuchi solitons on Fano admissible manifolds over the complex projective space $\mathbf{P}^{n}$.
title Mabuchi solitons and Mabuchi constants on Fano admissible manifolds
topic Differential Geometry
url https://arxiv.org/abs/2604.23261