Theorems · Theorem · global analysis

extDeriv_extDeriv

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {n : ℕ} {r : WithTop ℕ∞}
  {ω : E → E [⋀^Fin n]→L[𝕜] F}, ContDiff 𝕜 r ω → minSmoothness 𝕜 2 ≤ r → extDeriv (extDeriv ω) = 0

The second exterior derivative of a sufficiently smooth differential form is zero.

Defined in

Mathlib.Analysis.Calculus.DifferentialForm.Basic

Cited by

0 results in Mathlib

Foundations

Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace