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--Sasaki and certain Sasaki--Einstein manifolds, which arise for example as Boothby-Wang bundles over hyperk\"ahler and Calabi-Yau manifolds, respectively.
Keywords
Cite
@article{arxiv.2301.05914,
title = {A Bochner Technique For Foliations With Non-Negative Transverse Ricci Curvature},
author = {Leon Roschig},
journal= {arXiv preprint arXiv:2301.05914},
year = {2023}
}
Comments
After announcement Georges Habib pointed out that his article "Modified differentials and basic cohomology for Riemannian foliations" (MR3078356) with Ken Richardson contains a Bochner formula for the twisted Laplacian (Prop 6.7, Thm 6.16) which implies our Thm 4.4 even for non-harmonic foliations. The preprint will thus not be submitted for publication and will only appear in the author's thesis