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

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.

11 pages

References in corpus (3)

• Recent Progress on Ricci Solitons
• L^2 harmonics forms on non compact manifolds
• Geometry of manifolds with densities

Cited by in corpus (1)

• Harmonic aspects in an $\eta$-Ricci soliton