Towards Riemannian diffeology
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910010711212032 |
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| author | Kuribayashi, Katsuhiko Sakai, Keiichi Shiobara, Yusuke |
| author_facet | Kuribayashi, Katsuhiko Sakai, Keiichi Shiobara, Yusuke |
| contents | We introduce a framework for Riemannian diffeology. To this end, we use the tangent functor in the sense of Blohmann and one of the options of a metric on a diffeological space in the sense of Iglesias-Zemmour. As a consequence, the category consisting of weak Riemannian diffeological spaces and isometries is established. With a technical condition for a definite weak Riemannian metric, we show that the pseudodistance induced by the metric is indeed a distance. As examples of weak Riemannian diffeological spaces, an adjunction space of manifolds, a space of smooth maps and the mixed one are considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards Riemannian diffeology Kuribayashi, Katsuhiko Sakai, Keiichi Shiobara, Yusuke Differential Geometry Category Theory Geometric Topology Metric Geometry We introduce a framework for Riemannian diffeology. To this end, we use the tangent functor in the sense of Blohmann and one of the options of a metric on a diffeological space in the sense of Iglesias-Zemmour. As a consequence, the category consisting of weak Riemannian diffeological spaces and isometries is established. With a technical condition for a definite weak Riemannian metric, we show that the pseudodistance induced by the metric is indeed a distance. As examples of weak Riemannian diffeological spaces, an adjunction space of manifolds, a space of smooth maps and the mixed one are considered. |
| title | Towards Riemannian diffeology |
| topic | Differential Geometry Category Theory Geometric Topology Metric Geometry |
| url | https://arxiv.org/abs/2505.04170 |