广义的近凯勒-里奇孤子

IF 0.6 4区 数学 Q3 MATHEMATICS Differential Geometry and its Applications Pub Date : 2024-10-23 DOI:10.1016/j.difgeo.2024.102193
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引用次数: 0

摘要

我们将 Kähler-Ricci 孤子概括为近 Kähler 设定的井上矩图[25]的零点,并证明它们的存在阻碍了紧凑交映法诺流形上第一切恩-爱因斯坦近 Kähler 度量的存在。我们证明了 4 维情况下此类度量的变形结果。此外,我们还研究了 2n 维紧凑交折射法诺流形上全形向量场的李代数,它允许广义的近凯勒-里奇孤子。特别是,我们将松岛定理[41]部分扩展到了紧凑的第一切恩-爱因斯坦近凯勒流形。
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Generalized almost-Kähler–Ricci solitons
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.
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来源期刊
CiteScore
1.00
自引率
20.00%
发文量
81
审稿时长
6-12 weeks
期刊介绍: Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
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