Preprint A444/2006
On Yamabe constants of Riemannian products

Jimmy Petean | Akutagawa, Kazuo | Florit, Luis A.

**Keywords: **
Yamabe constant | product manifold

For a closed Riemannian manifold (M^m ,g) of constant positive
scalar curvature and any other closed Riemannian manifold (N^n ,h),
we show that the limit of the Yamabe constants of the Riemannian
products (M x N, g + r h) as r goes to infinity is equal to
the Yamabe constant of (M^m x R^n, [g + g_0])
and is strictly less than the Yamabe invariant of the sphere S^{m+n} for
n > 1. We then consider the minimum of the Yamabe functional
restricted to functions of the second variable and we compute the
limit in terms of the best constants of the Gagliardo-Nirenberg
inequalities.