  The important special case for which the function \(A^{i}_{2}(x^{i},  \gamma^{i}_{1})\) is a geodesic 4-acceleration field  corresponds to the affine structure of spacetime. For this special  case the function \(A^{i}_{2}(x^{i}, \gamma^{i}_{1}\))  is denoted by \(\Gamma^{i}_{2}(x^{i}, \gamma^{i}_{1}\)) and is given by 