Differential Geometry and Its Applications
We show how certain topological properties of co-Kähler manifolds derive from those of the Kähler manifolds which construct them. We go beyond Betti number results and describe the cohomology algebra structure of co-Kähler manifolds. As a consequence, we prove that co-Kähler manifolds satisfy the Toral Rank Conjecture: dim(H∗(M; Q)) ≥2r, for any r-torus Tr which acts almost freely on M.
Bazzoni, Giovanni; Lupton, Gregory; and Oprea, John F., "Hereditary Properties of Co-Kähler Manifolds" (2017). Mathematics Faculty Publications. 316.
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