Lie bracket of vector fields
= Lie bracket of vector fields
{wiki=Lie_bracket_of_vector_fields}
The Lie bracket of vector fields is an operation that takes two differentiable vector fields \\( X \\) and \\( Y \\) defined on a smooth manifold and produces another vector field, denoted \\( \[X, Y\] \\). This operation is essential in the study of the geometry of manifolds and plays a crucial role in various areas of differential geometry and mathematical physics.