Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex and Lagrangian surfaces of the complex projective plane via
  K\"ahlerian Killing Spin$^c$ spinors   The complex projective space $\mathbb C P^2$ of complex dimension $2$ has a
Spin$^c$ structure carrying K\"ahlerian Killing spinors. The restriction of one
of these K\"ahlerian Killing spinors to a surface $M^2$ characterizes the
isometric immersion of $M^2$ into $\mathbb C P^2$ if the immersion is either
Lagrangian or complex.

13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th