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arXiv · 1309.7648

Harmonic Forms on Manifolds with Non-Negative Bakry-Émery-Ricci Curvature

Matheus Vieira
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Abstract

In this paper we prove that on a complete smooth metric measure space with non-negative Bakry-Émery-Ricci curvature if the space of weighted L^2 harmonic one-forms is non-trivial then the weighted volume of the manifold is finite and universal cover of the manifold splits isometrically as the product of the real line with an hypersurface.

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Matheus Vieira. 2013-09-29. Harmonic Forms on Manifolds with Non-Negative Bakry-Émery-Ricci Curvature. https://arxiv.org/abs/1309.7648

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