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-$(\alpha,\delta) $-Sasaki and certain Sasaki-$ \eta $-Einstein manifolds, which arise for example as Boothby-Wang bundles over hyperkähler and Calabi-Yau manifolds, respectively.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2023
- DOI:
- arXiv:
- arXiv:2301.05914
- Bibcode:
- 2023arXiv230105914R
- Keywords:
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- Mathematics - Differential Geometry;
- 53C12;
- 53C25;
- 53C26
- E-Print:
- 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