Generalized almost-K\"ahler-Ricci solitons
Differential Geometry
2024-02-07 v1 Complex Variables
Abstract
We generalize K\"ahler-Ricci solitons to the almost-K\"ahler setting as the zeros of Inoue's moment map \cite{MR4017922}, and show that their existence is an obstruction to the existence of first-Chern-Einstein almost-K\"ahler metrics on compact symplectic Fano manifolds. We prove deformation results of such metrics in the -dimensional case. Moreover, we study the Lie algebra of holomorphic vector fields on -dimensional compact symplectic Fano manifolds admitting generalized almost-K\"ahler-Ricci solitons. In particular, we partially extend Matsushima's theorem \cite{MR0094478} to compact first-Chern-Einstein almost-K\"ahler manifolds.
Keywords
Cite
@article{arxiv.2402.03996,
title = {Generalized almost-K\"ahler-Ricci solitons},
author = {Michael Albanese and Giuseppe Barbaro and Mehdi Lejmi},
journal= {arXiv preprint arXiv:2402.03996},
year = {2024}
}