Morse-Novikov cohomology of almost nonnegatively curved manifolds

Abstract

Let Mn be a closed manifold of almost nonnegative sectional curvature and nonzero first de Rham cohomology group. Using a topological argument, we show that the Morse-Novikov cohomology group Hp(Mn,θ) vanishes for any p and [θ]∈HdR1(Mn),[θ]≠0. Based on a new integral formula, we also show that a similar result holds for a closed manifold of almost nonnegative Ricci curvature under the additional assumption that its curvature operator is uniformly bounded from below.