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

Teng Huang and Qiang Tan

Mathematische Nachrichten, 2021, vol. 294, issue 12, 2329-2339

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.

Date: 2021
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https://doi.org/10.1002/mana.202000065

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