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arXiv · 2501.04814

On foliations admitting a transverse similarity structure

Brice Flamencourt·Abdelghani Zeghib
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Abstract

We give a "conceptual" approach to Kourganoff's results about foliations with a transverse similarity structure. In particular, we give a proof, understandable by the targeted community, of the very important result classifying the holonomy of the closed, non-exact Weyl structures on compact manifolds, from which arose the notion of locally conformally product structures. We also extract from the proof several results on foliations admitting locally metric transverse connections.

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Brice Flamencourt, Abdelghani Zeghib. 2025-01-08. On foliations admitting a transverse similarity structure. https://arxiv.org/abs/2501.04814

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