_ds²_ = _g_^{στ} _d_ξ_{σ} _d_ξ_{τ}.
For any choice of the vectors _d_ξ_{σ} _d_ξ_{τ} this is scalar, and
_g_^{στ}, according to its definition is a symmetrical thing in σ and τ,
so it follows from the above results, that _g_^{στ} is a contravariant
tensor. Out of (16) it also follows that δ^{ν}_{μ} is a tensor which we
may call the mixed fundamental tensor.
_Determinant of the fundamental tensor._