δ(dxν/dλ) = (d/dλ)(δxν)
after partial integration,
{ λ₃
{ ∫ dλ kσ δxσ = 0
(20b) { λ₁
{
{ where kσ = (d/dλ){(gμν/ω) · (dxμ/dλ)} - (1/(2ω))(∂gμν/∂xσ
× (dxμ/dλ) · (dxν/dλ).
From which it follows, since the choice of δνσ is perfectly arbitrary that kσ’s should vanish. Then
(20c) kσ = 0 (σ = 1, 2, 3, 4)