Theorems · Theorem · differential geometry

Manifold.pathELength_def

∀ {E : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {H : Type u_5} [inst_2 : TopologicalSpace H]
  (I : ModelWithCorners ℝ E H) {M : Type u_6} [inst_3 : TopologicalSpace M] [inst_4 : ChartedSpace H M]
  [inst_5 : (x : M) → ENorm (TangentSpace I x)] (γ : ℝ → M) (a b : ℝ),
  Manifold.pathELength I γ a b = ∫⁻ (t : ℝ) in Set.Icc a b, ‖(mfderiv% γ t) 1‖ₑ

Defined in

Mathlib.Geometry.Manifold.Riemannian.PathELength

Cited by

3 results in Mathlib

Foundations

Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceENorm