Theorems · Definition · global analysis

VectorField.mlieBracket

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {H : Type u_2} →
      [inst_1 : TopologicalSpace H] →
        {E : Type u_3} →
          [inst_2 : NormedAddCommGroup E] →
            [inst_3 : NormedSpace 𝕜 E] →
              (I : ModelWithCorners 𝕜 E H) →
                {M : Type u_4} →
                  [inst_4 : TopologicalSpace M] →
                    [inst_5 : ChartedSpace H M] →
                      ((x : M) → TangentSpace I x) → ((x : M) → TangentSpace I x) → (x₀ : M) → TangentSpace I x₀

The Lie bracket of two vector fields in a manifold.

Defined in

Mathlib.Geometry.Manifold.VectorField.LieBracket

Cited by

32 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpace