Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geodesic-Einstein metrics and nonlinear stabilities   In this paper, we introduce notions of nonlinear stabilities for a relative
ample line bundle over a holomorphic fibration and define the notion of a
geodesic-Einstein metric on this line bundle, which generalize the classical
stabilities and Hermitian-Einstein metrics of holomorphic vector bundles. We
introduce a Donaldson type functional and show that this functional attains its
absolute minimum at geodesic-Einstein metrics, and we also discuss the
relations between the existence of geodesic-Einstein metrics and the nonlinear
stabilities of the line bundle. As an application, we will prove that a
holomorphic vector bundle admits a Finsler-Einstein metric if and only if it
admits a Hermitian-Einstein metric, which answers a problem posed by S.
Kobayashi.

18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph