Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spinors and the Weyl Tensor Classification in Six Dimensions   A spinorial approach to 6-dimensional differential geometry is constructed
and used to analyze tensor fields of low rank, with special attention to the
Weyl tensor. We perform a study similar to the 4-dimensional case, making full
use of the SO(6) symmetry to uncover results not easily seen in the tensorial
approach. Using spinors, we propose a classification of the Weyl tensor by
reinterpreting it as a map from 3-vectors to 3-vectors. This classification is
shown to be intimately related to the integrability of maximally isotropic
subspaces, establishing a natural framework to generalize the Goldberg-Sachs
theorem. We work in complexified spaces, showing that the results for any
signature can be obtained by taking the desired real slice.

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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ