Rotationally symmetric extremal pseudo-Kähler metrics of non-constant scalar curvatures

Xiaojuan, Duan

doi:10.1007/s12044-018-0376-5

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Radial Extremal Metrics1

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2020

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“…Even if its proof is known (see, for example, [1] and also [36]) we include it here for reader's convenience. A radial Kähler metric g is extremal if and only if…”

Section: Radial Extremal Metricsmentioning

confidence: 99%

Extremal Kaehler metrics induced by finite or infinite dimensional complex space forms

Loi,

Salis,

Zuddas

2020

Preprint

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In this paper we address the problem of studying those complex manifolds M equipped with extremal metrics g induced by finite or infinite dimensional complex space forms. We prove that when g is assumed to be radial and the ambient space is finite dimensional then (M, g) is itself a complex space form. We extend this result to the infinite dimensional setting by imposing the strongest assumption that the metric g has constant scalar curvature and is well-behaved (see Definition 1 in the Introduction). Finally, we analyze the radial Kähler-Einstein metrics induced by infinite dimensional elliptic complex space forms and we show that if such a metric is assumed to satisfy a stability condition then it is forced to have constant non-positive holomorphic sectional curvature.

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“…Even if its proof is known (see, for example, [1] and also [36]) we include it here for reader's convenience. A radial Kähler metric g is extremal if and only if…”

Section: Radial Extremal Metricsmentioning

confidence: 99%