Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The isometries of the space of K\"ahler metrics   Given a compact K\"ahler manifold, we prove that all global isometries of the
space of K\"ahler metrics are induced by biholomorphisms and
anti-biholomorphisms of the manifold. In particular, there exist no global
symmetries for Mabuchi's metric. Moreover, we show that the Mabuchi completion
does not even admit local symmetries. Closely related to these findings, we
provide a large class of metric geodesic segments that can not be extended at
one end, pointing out the first such examples in the literature.

32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph