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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