Harmonic Forms on Manifolds with Non-Negative Bakry-\'Emery-Ricci Curvature
Differential Geometry
2013-10-01 v1
Abstract
In this paper we prove that on a complete smooth metric measure space with non-negative Bakry-\'Emery-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.
Keywords
Cite
@article{arxiv.1309.7648,
title = {Harmonic Forms on Manifolds with Non-Negative Bakry-\'Emery-Ricci Curvature},
author = {Matheus Vieira},
journal= {arXiv preprint arXiv:1309.7648},
year = {2013}
}
Comments
11 pages