The geometry of Riemannian curvature radii
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909251923869696 |
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| author | Bellini, Eugenio |
| author_facet | Bellini, Eugenio |
| contents | In this paper we explore the geometric structures associated with curvature radii of curves with values on a Riemannian manifold $(M, g)$. We show the existence of sub-Riemannian manifolds naturally associated with the curvature radii and we investigate their properties. The main character of our construction is a pair of global vector fields $f_1, f_2$, which encodes intrinsic information about the geometry of $(M, g)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_11811 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The geometry of Riemannian curvature radii Bellini, Eugenio Differential Geometry 53C17 20F45 / 53C17 In this paper we explore the geometric structures associated with curvature radii of curves with values on a Riemannian manifold $(M, g)$. We show the existence of sub-Riemannian manifolds naturally associated with the curvature radii and we investigate their properties. The main character of our construction is a pair of global vector fields $f_1, f_2$, which encodes intrinsic information about the geometry of $(M, g)$. |
| title | The geometry of Riemannian curvature radii |
| topic | Differential Geometry 53C17 20F45 / 53C17 |
| url | https://arxiv.org/abs/2203.11811 |