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arXiv · 2402.03996

Generalized almost-K\"ahler-Ricci solitons

Michael Albanese·Giuseppe Barbaro·Mehdi Lejmi
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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 $4$-dimensional case. Moreover, we study the Lie algebra of holomorphic vector fields on $2n$-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.

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Michael Albanese, Giuseppe Barbaro, Mehdi Lejmi. 2024-02-06. Generalized almost-K\"ahler-Ricci solitons. https://arxiv.org/abs/2402.03996

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