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

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. [ABSTRACT FROM AUTHOR]