proposition 13.75 Invariance of the length

Rests on

• depends_on definition 13.73 Admissible change of parameter ¶
• depends_on definition 13.88 General coordinate transformation ¶
• 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 13.48 Differentiable manifold ¶
        • depends_on definition 13.47 Differentiable structure ¶
      • depends_on definition 13.84 Tensor ¶
        • depends_on definition 13.83 Covector ¶
        • depends_on definition 13.81 Vector on a manifold ¶
  • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶ ↺
  • depends_on definition 13.81 Vector on a manifold ¶ ↺
• proves proof ch:11-manifolds-tensors-curvature@proof-14 ¶

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