Let $M$ be a Manifold, $X$ be a Vector Field on the manifold $M$ and $F$ be a Foliation of the manifold $M$.
When is the vector field $X$ tangent to the foliation $F$?
2026-03-25 14:39:49.1774449589
Manifolds, Vector Fields and Foliations
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A foliation $F$ of a manifolds $M$ is a decomposition of $M$ into submanifolds $S$ (called the sheets of $F$) that are of dimension less of the dimension of $M$ and that a vector field $X$ be tangent to the sheets of the foliations: if $p\in S$ then $X(p)$ is in the tangent space $T_pS$.