Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anti-holomorphic involutive isometry of hyper-K\"ahler manifolds and
  branes   We study complex Lagrangian submanifolds of a compact hyper-K\"ahler manifold
and prove two results: (a) that an involution of a hyper-K\"ahler manifold
which is antiholomorphic with respect to one complex structure and which acts
non-trivially on the corresponding symplectic form always has a fixed point
locus which is complex Lagrangian with respect to one of the other complex
structures, and (b) there exist Lagrangian submanifolds which are complex with
respect to one complex structure and are not the fixed point locus of any
involution which is anti-holomorphic with respect to one of the other complex
structures.

21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph