We show that if  is a Riemannian foliation with dense leaves admitting a Lie extension on a compact connected manifold M, then  is Lie foliation having dense leaves.

More specifically, every Riemannian foliation  with dense leaves on a compact connected manifold M admitting a one-codimensional extension is a Lie foliation having dense leaves.

foliation, Riemannian foliation, Riemannian foliation having dense leaves, extension of foliation, foliated vector fields, structural Lie algebra of Riemannian foliation.

Received: April 17, 2022; Revised: June 4, 2022; Accepted: June 21, 2022; Published: July 7, 2022

How to cite this article: Cyrille Dadi, Dense leaf Riemannian foliation admitting a Lie extension on a compact connected manifold, JP Journal of Geometry and Topology 27 (2022), 49-66. http://dx.doi.org/10.17654/0972415X22004

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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