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- Title
Extremal Kähler Metrics Induced by Finite or Infinite-Dimensional Complex Space Forms.
- Authors
Loi, Andrea; Salis, Filippo; Zuddas, Fabio
- 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 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 nonpositive holomorphic sectional curvature.
- Publication
Journal of Geometric Analysis, 2021, Vol 31, Issue 8, p7842
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-020-00554-4