Theorems · Theorem · global analysis

isMIntegralCurve_const

∀ {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]
  {v : (x : M) → TangentSpace I x} {x : M}, v x = 0 → IsMIntegralCurve (fun x_1 => x) v

If the vector field v vanishes at x₀, then the constant curve at x₀ is a global integral curve of v.

Defined in

Mathlib.Geometry.Manifold.IntegralCurve.Transform

Cited by

0 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace