Building a Riemannian metric through perscribed Christoffel symbols

Question

Suppose I have $d^3$ many class $C^{1}$ functions $f_{i,j,k}:\mathbb{R}^d\rightarrow \mathbb{R}$. Are there precise requirements on $f_{i,j,k}$ in order for there to exist a Riemannian metric $g_t$ on $\mathbb{R}^d$ whose Christoffel symbols $$ \Gamma_{i,j}^k = f_{i,j,k}? $$