L2-Harmonic Forms on Incomplete Riemannian Manifolds with Positive Ricci Curvature

Abstract

Abstract:We construct an incomplete Riemannian manifold with positive Ricci curvature that has non-trivial L 2 -harmonic forms and on which the L 2 -Stokes theorem does not hold. Therefore, a Bochner-type vanishing theorem does not hold for incomplete Riemannian manifolds.