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

Teng Huang; Qiang Tan

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arXiv · 1904.09436

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

Teng Huang·Qiang Tan

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Abstract

In this article, we first consider the $L^{2}$ \textit{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 $L^{2}$ \textit{Morse-Novikov cohomology}, we prove that the $L^{2}$-harmonic forms on $M$ are identically zero.

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BibTeX RIS

Teng Huang, Qiang Tan. 2020-05-28. Vanishing theorems on complete Riemannian manifold with a parallel $1$-form. https://arxiv.org/abs/1904.09436

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