JP Journal of Geometry and Topology

The JP Journal of Geometry and Topology publishes articles in all branches of geometry and topology, with applications to physics. It covers areas such as differential geometry, algebraic topology, and geometric aspects of mathematical physics. Survey articles are also welcome.

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DENSE LEAF RIEMANNIAN FOLIATION ADMITTING A LIE EXTENSION ON A COMPACT CONNECTED MANIFOLD

Authors

  • Cyrille Dadi

Keywords:

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

DOI:

https://doi.org/10.17654/0972415X22004

Abstract

We show that if $\mathcal{F}$  is a Riemannian foliation with dense leaves admitting a Lie extension on a compact connected manifold $M$, then $\mathcal{F}$  is Lie foliation having dense leaves.

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

Received: April 17, 2022 
Revised: June 4, 2022 
Accepted: June 21, 2022

References

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C. Dadi, Sur les extensions des feuilletages, Thèse unique, Université de Cocody, Abidjan, 2008.

C. Dadi and A. Codjia, Riemannian foliation with dense leaves on a compact manifold, Int. J. Math. Comput. Sci. 11(2) (2016), 151-172.

C. Dadi and A. Codjia, Foliated fields of an extension of a Lie G-foliation having dense leaves on a compact manifold, Far East J. Math. Sci. (FJMS) 107(2) (2018), 357-385.

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A. El Kacimi Alaoui, G. Guasp and M. Nicolau, On deformations of transversely homogeneous foliations, Prépublication, UAB, 4, 1999.

E. Fédida, Sur l’existence des feuilletages de Lie, C. R. Acad. Sci. Paris Sér. A 278 (1974), 835-837 (in French).

C. Godbillon, Feuilletage, Etude géométriques I, Publ. IRMA, Strasbourg, 1985.

P. Molino, Riemannian Foliations, Birkhäuser, 1988.

T. Masson, Géométrie différentielle, groupes et algèbres de Lie, fibrés et connexions, Laboratoire de Physique Théorique, Université Paris XI, Bâtiment 210, 91405 Orsay Cedex, France, 2001.

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Published

2022-07-07

Issue

Vol. 27 (2022)

Section

Articles

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How to Cite

DENSE LEAF RIEMANNIAN FOLIATION ADMITTING A LIE EXTENSION ON A COMPACT CONNECTED MANIFOLD. (2022). JP Journal of Geometry and Topology, 27, 49-66. https://doi.org/10.17654/0972415X22004

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