## Cohomologie $$L^ p$$ des variétés à courbure négative, cas du degré 1. $$(L^ p$$-cohomology of manifolds of negative curvature, the case of degree 1).(French)Zbl 0723.53023

Rend. Semin. Mat., Torino Fasc. Spec., 95-120 (1989).
In this paper the $$L^ p$$-cohomology of degree 1 of Riemannian manifolds is studied. It is shown that for manifolds with a positive lower bound for the injectivity radius and with a lower bound for the Ricci curvature the $$L^ p$$-cohomology is invariant under quasi isometries. Then bounds are given for the numbers p such that the $$L^ p$$-cohomology vanishes for a homogeneous manifold of negative sectional curvature resp. for a manifold with negative sectional curvature pinched between two negative constants.

### MSC:

 53C20 Global Riemannian geometry, including pinching