Theorems · Theorem · global analysis

tangentBundle_model_space_chartAt

∀ {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}
  (p : TangentBundle I H), (chartAt (ModelProd H E) p).toPartialEquiv = (Bundle.TotalSpace.toProd H E).toPartialEquiv

In the tangent bundle to the model space, the charts are just the canonical identification between a product type and a sigma type, a.k.a. TotalSpace.toProd.

Defined in

Mathlib.Geometry.Manifold.VectorBundle.Tangent

Cited by

4 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpace