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- W2015719180 abstract "HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button. We classify quadruples $(M, g, m, tau)$ in which (M, g) is a compact Kähler manifold of complex dimension m > 2 and $tau$ is a nonconstant function on M such that the conformally related metric $g/tau^{2}$, defined wherever $tau ne 0$, is an Einstein metric. It turns out that M then is the total space of a holomorphic $mathbb{C}{rm P}^1$ bundle over a compact Kähler–Einstein manifold (N, h). The quadruples in question constitute four disjoint families: one, well known, with Kähler metrics g that are locally reducible; a second, discovered by Bérard Bergery (1982), and having $tau ne 0$ everywhere; a third one, related to the second by a form of analytic continuation, and analogous to some known Kähler surface metrics; and a fourth family, present only in odd complex dimensions $m ge 9$. Our classification uses a moduli curve, which is a subset $mathcal{C}$, depending on m, of an algebraic curve in $mathbb{R}^2$. A point (u, v) in $mathcal{C}$ is naturally associated with any $(M, g, m, tau)$ having all of the above properties except for compactness of M, replaced by a weaker requirement of ‘vertical’ compactness. One may in turn reconstruct M, g and $tau$ from (u, v) coupled with some other data, among them a Kähler–Einstein base (N, h) for the $mathbb{C}{rm P}^1$ bundle M. The points (u, v) arising in this way from $(M, g, m, tau)$ with compactM form a countably infinite subset of mathcal{C}$." @default.
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- W2015719180 date "2005-06-21" @default.
- W2015719180 modified "2023-10-14" @default.
- W2015719180 title "A moduli curve for compact conformally-Einstein Kähler manifolds" @default.
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- W2015719180 doi "https://doi.org/10.1112/s0010437x05001612" @default.
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