Subbundle

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A subbundle $L$ of a vector bundle $E$ over a topological space $M$.

In mathematics, a subbundle $L$ of a vector bundle $E$ over a topological space $M$ is a collection of linear subspaces $L_x$of the fibers $E_x$ of $E$ at $x$ in $M,$ that make up a vector bundle in their own right.

In connection with foliation theory, a subbundle of the tangent bundle of a smooth manifold may be called a distribution (of tangent vectors).

If locally, in a neighborhood $N_x$ of $x\in M$, a set of vector fields $Y_k$ span the vector spaces $L_y,y\in N_x,$ and all Lie commutators $[Y_i,Y_j]$ are linear combinations of $Y_1,\dots ,Y_n$ then one says that $L$ is an involutive distribution.

See also

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