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structure definition def or abbrev

RealGeodesic

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formal statement (Lean)

 110structure RealGeodesic (g : MetricTensor) where
 111  path : ℝ → (Fin 4 → ℝ)
 112  geodesic_equation : ∀ lam μ,
 113    deriv (deriv (fun lam' => path lam' μ)) lam +
 114    Finset.sum Finset.univ (fun ρ =>
 115      Finset.sum Finset.univ (fun σ =>
 116        christoffel g (path lam) μ ρ σ *
 117        (deriv (fun lam' => path lam' ρ) lam) *
 118        (deriv (fun lam' => path lam' σ) lam))) = 0
 119
 120/-- A timelike geodesic: path with negative interval, using real Christoffel. -/

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