Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal Kaehler metrics induced by finite or infinite dimensional
  complex space forms   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.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org