Description
Initially defined in the context of General Relativity, the ADM mass is an important invariant of Riemannian asymptotically flat manifolds. Some 25 years ago, L. Habermann used it to answer a question in pure Riemannian geometry : finding a canonical metric in each conformal class of Riemannian metrics with positive scalar curvature on a compact manifold of dimension 3, 4, or 5. Despite the importance of the question in geometry, the Habermann metric seems to have escaped further notice. In a joint work with Emmanuel Humbert (Tours), we study its volume, which may lead to an interesting new topological invariant of low-dimensional manifolds.