Isomorphism for the Holonomy Group of a K-Contact Sub-Riemannian Space
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915418479788032 |
|---|---|
| author | Kokin, Evgenii |
| author_facet | Kokin, Evgenii |
| contents | The holonomy group of the adapted connection on a K-contact Riemannian manifold $(M, θ, g)$ is considered. It is proved that if the orbit space $M/ξ$ of the Reeb field $ξ$ action admits a manifold structure, then the holonomy group of the adapted connection on $M$ is isomorphic to the holonomy group of the Levi-Civita connection on the Riemannian manifold $(M/ξ, h)$, where $h$ is the induced Riemannian metric on $M/ξ$. Thanks to this result, a simple proof of the de Rham theorem for the case of K-contact sub-Riemannian manifolds is obtained, stating that if the holonomy group of the adapted connection on $M$ is not irreducible, then the orbit space $M/ξ$ is locally a product of Riemannian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isomorphism for the Holonomy Group of a K-Contact Sub-Riemannian Space Kokin, Evgenii Differential Geometry The holonomy group of the adapted connection on a K-contact Riemannian manifold $(M, θ, g)$ is considered. It is proved that if the orbit space $M/ξ$ of the Reeb field $ξ$ action admits a manifold structure, then the holonomy group of the adapted connection on $M$ is isomorphic to the holonomy group of the Levi-Civita connection on the Riemannian manifold $(M/ξ, h)$, where $h$ is the induced Riemannian metric on $M/ξ$. Thanks to this result, a simple proof of the de Rham theorem for the case of K-contact sub-Riemannian manifolds is obtained, stating that if the holonomy group of the adapted connection on $M$ is not irreducible, then the orbit space $M/ξ$ is locally a product of Riemannian manifolds. |
| title | Isomorphism for the Holonomy Group of a K-Contact Sub-Riemannian Space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.23090 |