theorem 13.79 Frenet–Serret equations, covariant form

Rests on

• depends_on definition 13.149 Metric compatibility ¶
  • depends_on definition 13.145 Affine connection ¶
    • depends_on definition 13.90 Mixed tensor ¶
      • depends_on definition 13.89 Contravariant and covariant tensors ¶
        • depends_on definition 13.88 General coordinate transformation ¶
      • depends_on definition 13.88 General coordinate transformation ¶ ↺
    • depends_on definition 13.82 Vector field ¶
      • depends_on definition 13.81 Vector on a manifold ¶
        • depends_on definition 13.71 Differentiable curve ¶
        • depends_on definition 13.45 Differentiable map on a topological space ¶
        • depends_on definition 13.48 Differentiable manifold ¶
  • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶
    • depends_on definition 13.48 Differentiable manifold ¶ ↺
    • depends_on definition 13.84 Tensor ¶
      • depends_on definition 13.83 Covector ¶
        • depends_on definition 13.81 Vector on a manifold ¶ ↺
      • depends_on definition 13.81 Vector on a manifold ¶ ↺
  • depends_on definition 13.146 Parallel transport and autoparallels ¶
    • depends_on definition 13.145 Affine connection ¶ ↺
• depends_on equation 13.172 eq:mfd-binormal-intrinsic ¶
• depends_on proposition 13.78 The curvature vector is orthogonal to the tangent ¶
  • depends_on definition 13.77 Curvature vector ¶
    • depends_on definition 13.76 Arclength parametrisation ¶
      • depends_on definition 13.73 Admissible change of parameter ¶
      • depends_on definition 13.74 Length of a curve ¶
        • depends_on definition 13.118 Line element ¶
        • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶ ↺
        • depends_on definition 13.81 Vector on a manifold ¶ ↺
    • depends_on definition 13.145 Affine connection ¶ ↺
    • depends_on theorem 13.150 Levi-Civita connection and contorsion ¶
      • depends_on definition 13.145 Affine connection ¶ ↺
      • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶ ↺
      • depends_on definition 13.149 Metric compatibility ¶ ↺
      • depends_on definition 13.147 Torsion ¶
        • depends_on definition 13.145 Affine connection ¶ ↺
      • proves proof ch:11-manifolds-tensors-curvature@proof-41 ¶
  • depends_on definition 13.149 Metric compatibility ¶ ↺
  • depends_on equation 13.170 eq:mfd-unit-tangent-intrinsic ¶
  • proves proof ch:11-manifolds-tensors-curvature@proof-15 ¶
• proves proof ch:11-manifolds-tensors-curvature@proof-16 ¶

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