Collapsing regular Riemannian foliations with flat leaves
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908767814156288 |
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| author | Corro, Diego |
| author_facet | Corro, Diego |
| contents | In this manuscript we present how to collapse a manifold equipped with a closed flat regular Riemannian foliation with leaves of positive dimension, while keeping the sectional curvature uniformly bounded from above and below. From this deformation, we show that in the case when the manifold is compact and simply connected the foliation is given by torus actions. This gives a geometric characterization of aspherical regular Riemannian foliations given by torus actions |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11602 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Collapsing regular Riemannian foliations with flat leaves Corro, Diego Differential Geometry 53C12, 53C23, 53C20, 57R30, 53C24 In this manuscript we present how to collapse a manifold equipped with a closed flat regular Riemannian foliation with leaves of positive dimension, while keeping the sectional curvature uniformly bounded from above and below. From this deformation, we show that in the case when the manifold is compact and simply connected the foliation is given by torus actions. This gives a geometric characterization of aspherical regular Riemannian foliations given by torus actions |
| title | Collapsing regular Riemannian foliations with flat leaves |
| topic | Differential Geometry 53C12, 53C23, 53C20, 57R30, 53C24 |
| url | https://arxiv.org/abs/2403.11602 |