Generalized almost-Kähler-Ricci solitons

2024/02/06 by Michael Albanese, Albanese, Michael, Giuseppe Bárbaro +3
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2402.03996

Abstract

We generalize Kähler-Ricci solitons to the almost-Kähler setting as the zeros of Inoue's moment map \citeMR4017922, and show that their existence is an obstruction to the existence of first-Chern-Einstein almost-Kähler metrics on compact symplectic Fano manifolds. We prove deformation results of such metrics in the 4-dimensional case. Moreover, we study the Lie algebra of holomorphic vector fields on 2n-dimensional compact symplectic Fano manifolds admitting generalized almost-Kähler-Ricci solitons. In particular, we partially extend Matsushima's theorem \citeMR0094478 to compact first-Chern-Einstein almost-Kähler manifolds.

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