Finiteness of $\pi_1$ and geometric inequalities in almost positive Ricci curvature.

Erwann Aubry (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We show that complete $n$-manifolds whose part of Ricci curvature less than a positive number is small in $L^p$ norm (for $p>n/2$) have bounded diameter and finite fundamental group. On the contrary, complete metrics with small $L^{n/2}$-norm of the same part of the Ricci curvature are dense in the set of metrics of any compact differentiable manifold.

Mots clés: Ricci curvature; comparison theorems; fundamental group

Domaines: Géométrie différentielle [math.DG]

Erwann Aubry. Finiteness of $\pi_1$ and geometric inequalities in almost positive Ricci curvature.. Annales Scientifiques de l'École Normale Supérieure, 2007, 40 (4), pp.675-695. ⟨hal-00338175⟩