针对具有非负横截Ricci曲率的叶状结构的Bochner技术
微分几何
2023-01-31 v2
摘要
我们将Bochner技术推广至具有非负横截Ricci曲率的叶状结构。特别地，我们得到了一个关于基本上同调的新消没定理。随后，我们给出两个自然应用，即针对退化3--Sasaki流形和某些Sasaki--Einstein流形的应用，它们分别作为超kähler流形和Calabi-Yau流形上的Boothby-Wang丛出现。
引用
@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}
}
备注
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