We can calculate the curvature tensor and sectional curvature using Christoffel symbols. However, can we express Christoffel symbols using curvature or sectional curvature? Is there a specific equation, such as $\Gamma_{ij}^k = f(Curvature)$?
There is no known explicit expression for the Christoffel symbol as a function of curvature or sectional curvature. Are there any special cases where the Christoffel symbol can be expressed in terms of curvature or sectional curvature?