Extremal Kaehler metrics induced by finite or infinite dimensional complex space forms
| Autor: | Loi, Andrea, Salis, Filippo, Zuddas, Fabio |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 24 pages |
| Databáze: | arXiv |
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