On foliations admitting a transverse similarity structure

TL;DR

This paper provides a clear, conceptual proof of the classification of holonomy in foliations with transverse similarity structures, advancing understanding of locally conformally product structures and related foliations.

Contribution

It offers an accessible proof of key classification results and derives new insights on foliations with locally metric transverse connections.

Findings

Classification of holonomy for closed, non-exact Weyl structures.

Insights into foliations with locally metric transverse connections.

Clarification of the structure of locally conformally product foliations.

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.