Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partner symmetries of the complex Monge-Ampere equation yield
  hyper-Kahler metrics without continuous symmetries   We extend the Mason-Newman Lax pair for the elliptic complex Monge-Amp\`ere
equation so that this equation itself emerges as an algebraic consequence. We
regard the function in the extended Lax equations as a complex potential. We
identify the real and imaginary parts of the potential, which we call partner
symmetries, with the translational and dilatational symmetry characteristics
respectively. Then we choose the dilatational symmetry characteristic as the
new unknown replacing the K\"ahler potential which directly leads to a Legendre
transformation and to a set of linear equations satisfied by a single real
potential. This enables us to construct non-invariant solutions of the Legendre
transform of the complex Monge-Amp\`ere equation and obtain hyper-K\"ahler
metrics with anti-self-dual Riemann curvature 2-form that admit no Killing
vectors.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat