Manifolds of Riemannian metrics with prescribed scalar curvature
Fischer, A. E. and J. E. Marsden
Bull. Amer. Math. Soc., 80, (1974), 479-484
Abstract:
Throughout, M
will denote a
C
compact connected oriented n
-manifold, n 2
. Let
: M
be a
C
function,
the space of
C
riemannian metrics on M
and
= {g : R(g) = }
where R(g)
is the scalar curvature of g
. A superscript s
will denote objects in the corresponding Sobolev space,
s > n + 1
(one can also treat Ws, p
spaces in the same way), and we also allow s =
so
=
.