Theorems · Theorem · differential geometry

Manifold.pathELength_add

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {H : Type u_2} [inst_2 : TopologicalSpace H]
  {I : ModelWithCorners ℝ E H} {M : Type u_3} [inst_3 : TopologicalSpace M] [inst_4 : ChartedSpace H M]
  [inst_5 : (x : M) → ENorm (TangentSpace I x)] {a b c : ℝ} {γ : ℝ → M},
  a ≤ b → b ≤ c → Manifold.pathELength I γ a b + Manifold.pathELength I γ b c = Manifold.pathELength I γ a c

Defined in

Mathlib.Geometry.Manifold.Riemannian.PathELength

Cited by

1 results in Mathlib

Foundations

Depth 248 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceENorm