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 hyperkähler and Calabi-Yau manifolds, respectively.