English

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