proposition 21.73 Free motion in flat spacetime, any coordinates

Rests on

• depends_on equation 21.75 eq:lag-geodesic ¶
• depends_on equation 21.79 eq:lag-relativistic-action ¶
• depends_on theorem 13.150 Levi-Civita connection and contorsion ¶
  • 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 13.149 Metric compatibility ¶
    • depends_on definition 13.145 Affine connection ¶ ↺
    • depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶ ↺
    • depends_on definition 13.146 Parallel transport and autoparallels ¶
      • depends_on definition 13.145 Affine connection ¶ ↺
  • depends_on definition 13.147 Torsion ¶
    • depends_on definition 13.145 Affine connection ¶ ↺
  • proves proof ch:11-manifolds-tensors-curvature@proof-41 ¶
• proves proof ch:04-lagrangian-mechanics@proof-18 ¶

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