Generalized almost-Kähler–Ricci solitons

TY - JOUR

T1 - Generalized almost-Kähler–Ricci solitons

AU - Albanese, Michael

AU - Barbaro, Giuseppe

AU - Lejmi, Mehdi

N1 - Publisher Copyright: © 2024 Elsevier B.V.

PY - 2024/12

Y1 - 2024/12

N2 - We generalize Kähler–Ricci solitons to the almost-Kähler setting as the zeros of Inoue's moment map [25], 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 [41] to compact first-Chern–Einstein almost-Kähler manifolds.

AB - We generalize Kähler–Ricci solitons to the almost-Kähler setting as the zeros of Inoue's moment map [25], 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 [41] to compact first-Chern–Einstein almost-Kähler manifolds.

UR - http://www.scopus.com/inward/record.url?scp=85207128950&partnerID=8YFLogxK

U2 - 10.1016/j.difgeo.2024.102193

DO - 10.1016/j.difgeo.2024.102193

M3 - Journal article

AN - SCOPUS:85207128950

SN - 0926-2245

VL - 97

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

M1 - 102193

ER -