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<p>We present a “conceptual” approach to Kourganoff’s results on foliations with a transverse similarity structure. We provide a geometric proof, based on the linearization of the holonomy and accessible to researchers in conformal geometry, of these results. In particular, we recover the main theorem classifying the holonomy of closed, non-exact Weyl structures on compact manifolds, from which the notion of locally conformally product structures arose. We also extract from the proof several results on foliations admitting locally metric transverse connections.</p>

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On foliations admitting a transverse similarity structure

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Brice Flamencourt,
  • Abdelghani Zeghib

摘要

We present a “conceptual” approach to Kourganoff’s results on foliations with a transverse similarity structure. We provide a geometric proof, based on the linearization of the holonomy and accessible to researchers in conformal geometry, of these results. In particular, we recover the main theorem classifying the holonomy of closed, non-exact Weyl structures on compact manifolds, from which the notion of locally conformally product structures arose. We also extract from the proof several results on foliations admitting locally metric transverse connections.