Theorems · Definition · global analysis

tangentBundleCore

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {H : Type u_4} →
            [inst_3 : TopologicalSpace H] →
              (I : ModelWithCorners 𝕜 E H) →
                (M : Type u_6) →
                  [inst_4 : TopologicalSpace M] →
                    [inst_5 : ChartedSpace H M] → [IsManifold I 1 M] → VectorBundleCore 𝕜 M E ↑(atlas H M)

Let M be a C^1 manifold with model I on (E, H). Then tangentBundleCore I M is the vector bundle core for the tangent bundle over M. It is indexed by the atlas of M, with fiber E and its change of coordinates from the chart i to the chart j at point x : M is the derivative of the composite `` I.symm i.symm j I E --> H --> M --> H --> E ` within the set range I ⊆ E at I (i x) : E`.

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Tangent

Cited by

25 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold