Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: La Grassmannienne non-lin\'eaire comme vari\'et\'e fr\'ech\'etique
  homog\`ene   Let (M,g) be a compact Riemannian manifold of dimension n. For k \in
{0,...,n}, we denote Gr_{k}(M) the set of compact, connected and oriented
submanifolds of M of dimension k. This set is called the non-linear
Grassmannian. In this article, we endow Gr_{k}(M) with a smooth Fr\'echet
manifold structure and investigate its basic geometrical properties. In
particular, if \Sigma \in Gr_{k}(M), we show that the space of smooth
embeddings Emb(\Sigma,M) is the total space of principal fiber bundle with base
space a collection of connected components of Gr_{k}(M). We also show that the
connected components of Gr_{k}(M) are homogeneous with respect to the natural
action of the group of diffeomorphisms of M.

31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an