Vanishing theorems on complete Riemannian manifold with a parallel 1-form

2019/04/20 by Huang, Teng, Tan, Qiang
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.09436

Abstract

In this article, we first consider the L² Morse-Novikov cohomology on a complete Riemannian manifold M equipped with a parallel 1-form which includes Vaisman manifold. Based on a vanishing theorem of L² Morse-Novikov cohomology, we prove that the L²-harmonic forms on M are identically zero.

Related

• Vanishing theorems for L² harmonic forms on complete Riemannian manifolds
• Vanishing properties of p-harmonic ℓ-forms on Riemannian manifolds
• On the cohomology of L²-harmonic forms of an incomplete Riemannian manifold
• Lp -cohomology and the geometry of p-harmonic forms
• Vanishing theorems of the basic harmonic forms on a complete foliated Riemannian manifold