In [1, 2], we showed that any extension of a Lie -foliation having dense leaves on a compact connected manifold M corresponds to a  Lie subalgebra  of  In this paper, we determine the Lie algebra  of -transverse foliated vector fields of an extension corresponding to the subalgebra  Noting by  the -transverse foliated vector field associated to    we prove that

foliation, foliation having its dense leaves, extension of foliation, Lie foliation, Lie algebra, Lie subalgebra, Lie group, Lie subgroup, local central transverse vector field, local Killing transverse vector field, locally constant sheaf of germs of local transverse Killing vector fields.

Received: May 6, 2022; Revised: August 11, 2022; Accepted: August 20, 2022; Published: September 21, 2022

How to cite this article: Cyrille Dadi, Determining Lie algebra of transverse foliated vector field of the extension of dense leaf Lie foliation on a compact connected manifold, Universal Journal of Mathematics and Mathematical Sciences 16 (2022), 21-39. http://dx.doi.org/10.17654/2277141722007

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References:

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