Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sobolev metrics on the manifold of all Riemannian metrics   On the manifold $\Met(M)$ of all Riemannian metrics on a compact manifold $M$
one can consider the natural $L^2$-metric as described first by \cite{Ebin70}.
In this paper we consider variants of this metric which in general are of
higher order. We derive the geodesic equations, we show that they are
well-posed under some conditions and induce a locally diffeomorphic geodesic
exponential mapping. We give a condition when Ricci flow is a gradient flow for
one of these metrics.

29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom