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- W4283205596 abstract "A compact complex Hermitian manifold $(M, I, w)$ is called Vaisman if $dw=wwedge theta$ and the 1-form $theta$, called the Lee form, is parallel with respect to the Levi-Civita connection. The volume form of $M$ is invariant with respect to the action of the vector field $X$ dual to $theta$ (called the Lee field) and the vector field $I(X)$, called { the anti-Lee field}. The cohomology class of $theta$, called the Lee class, plays the same role as the Kahler class in Kahler geometry. We prove that a Vaisman metric is uniquely determined by its volume form and the Lee class, and, conversely, for each Lee class $[theta]$ and each Lee- and anti-Lee-invariant volume form $V$, there exists a Vaisman structure with the volume form $V$ and the Lee class $c[theta]$. This is an analogue of the Calabi-Yau theorem claiming that the Kahler form is uniquely determined by its volume and the cohomology class." @default.
- W4283205596 created "2022-06-22" @default.
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- W4283205596 date "2022-06-17" @default.
- W4283205596 modified "2023-09-27" @default.
- W4283205596 title "A Calabi-Yau theorem for Vaisman manifolds" @default.
- W4283205596 doi "https://doi.org/10.48550/arxiv.2206.08808" @default.
- W4283205596 hasPublicationYear "2022" @default.
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