L 2 -Harmonic Forms on Incomplete Riemannian Manifolds with Positive Ricci Curvature

Junya Takahashi
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Junya Takahashi: Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tôhoku University, 6-3-09, Aoba, Sendai 980-8579, Japan

Mathematics, 2018, vol. 6, issue 5, 1-11

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.

Keywords: L 2 -harmonic forms; Hodge–Laplacian; manifold with singularity; L 2 -Stokes theorem; capacity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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