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

Andrea Loi; Filippo Salis; Fabio Zuddas

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arXiv · 2006.02101

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

Andrea Loi·Filippo Salis·Fabio Zuddas

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Abstract

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 Kaehler-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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BibTeX RIS

Andrea Loi, Filippo Salis, Fabio Zuddas. 2020-06-03. Extremal Kaehler metrics induced by finite or infinite dimensional complex space forms. https://arxiv.org/abs/2006.02101

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