Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Calibrated Submanifolds of R^7 and R^8 with Symmetries   The principal theory of this paper comprises a technique for constructing
associative, coassociative and Cayley submanifolds of Euclidean space with
symmetries, using first-order ordinary differential equations. Explicit
examples of U(1)-invariant associative cones in R^7 and SU(2)-invariant Cayley
4-folds in R^8 are then produced using this method. Further examples of
associative 3-folds are presented, which are ruled, and other systems of
differential equations defining calibrated submanifolds in R^7 and R^8 are
given.

8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat