Theorems · Definition · global analysis

IsMIntegralCurveAt

{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] → (ℝ → M) → ((x : M) → TangentSpace I x) → ℝ → Prop

If v is a vector field on M and t₀ : ℝ, IsMIntegralCurveAt γ v t₀ means γ : ℝ → M is a local integral curve of v in a neighbourhood containing t₀. The value of γ outside of this interval is irrelevant and considered junk.

Defined in

Mathlib.Geometry.Manifold.IntegralCurve.Basic

Cited by

19 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace