D l a = ( ε ε + ε ε ¯ ¯ ) l a − − κ κ ¯ ¯ m a − − κ κ m ¯ ¯ a shows that l a is tangent to a geodesic if and only if κ κ = 0 , and is tangent to an affinely parameterized geodesic if in addition ( ε ε + ε ε ¯ ¯ ) = 0 . Similarly, Δ Δ n a = ν ν m a + ν ν ¯ ¯ m ¯ ¯ a − − ( γ γ + γ γ ¯ ¯ ) n a shows that n a is geodesic if and only if ν ν = 0 , and has affine parameterization when ( γ γ + γ γ ¯ ¯ ) = 0 .