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Vanishing theorems on complete Riemannian manifold with a parallel $1$-form
- Publication Year :
- 2019
-
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.<br />Comment: 13 pages; to appear in Mathematische Nachrichten
- Subjects :
- Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1904.09436
- Document Type :
- Working Paper