Theorems · Definition · differential geometry

IsCovariantDerivativeOn.torsion

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {H : Type u_3} →
            [inst_3 : TopologicalSpace H] →
              {I : ModelWithCorners 𝕜 E H} →
                {M : Type u_4} →
                  [inst_4 : TopologicalSpace M] →
                    [inst_5 : ChartedSpace H M] →
                      [inst_6 : IsManifold I 2 M] →
                        [CompleteSpace E] →
                          {cov : ((x : M) → TangentSpace I x) → (x : M) → TangentSpace I x →L[𝕜] TangentSpace I x} →
                            [CompleteSpace 𝕜] →
                              [FiniteDimensional 𝕜 E] →
                                IsCovariantDerivativeOn E cov →
                                  (x : M) → TangentSpace I x →L[𝕜] TangentSpace I x →L[𝕜] TangentSpace I x

The torsion tensor of an unbundled covariant derivative on TM.

Defined in

Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Torsion

Cited by

5 results in Mathlib

Foundations

Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifoldCompleteSpaceCompleteSpaceFiniteDimensional