The Principle of Relativity

by Albert Einstein; H. Minkowski

By mixed multiplication with g^στ and g_νλ respectively we obtain (changing the mode of writing the indices).

dg^μν = -g^μα g^νβ dg_αβ

∂g^μν/∂x_σ = -g^μα g^νβ dg_αβ

and

(32)

dg_μν = -g_μα g_νβ dg^αβ

∂g_μν/∂x_σ = -g_μα g_νβ ∂g^αβ/∂x_σ.

The expression (31) allows a transformation which we shall often use; according to (21)