Theorems · Theorem · global analysis

TangentBundle.chartAt_toPartialEquiv

∀ {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] [inst_6 : IsManifold I 1 M] (p : TangentBundle I M),
  (chartAt (ModelProd H E) p).toPartialEquiv =
    ((tangentBundleCore I M).toFiberBundleCore.localTrivAsPartialEquiv (achart H p.proj)).trans
      ((chartAt H p.proj).prod (PartialEquiv.refl E))

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Tangent

Cited by

0 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold