A Bochner Technique For Foliations With Non-Negative Transverse Ricci Curvature
Abstract
We generalize the Bochner technique to foliations with non-negative transverse Ricci curvature. In particular, we obtain a new vanishing theorem for basic cohomology. Subsequently, we provide two natural applications, namely to degenerate 3-(α,δ) -Sasaki and certain Sasaki- η -Einstein manifolds, which arise for example as Boothby-Wang bundles over hyperk\"ahler and Calabi-Yau manifolds, respectively.
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