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arXiv · 2505.04170

Towards Riemannian diffeology

Katsuhiko Kuribayashi·Keiichi Sakai·Yusuke Shiobara
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Abstract

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.

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Katsuhiko Kuribayashi, Keiichi Sakai, Yusuke Shiobara. 2025-05-07. Towards Riemannian diffeology. https://doi.org/10.1017/prm.2025.10114

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