### Metric Tensors and Christoffel Symbols

Problem 1. Derive the formula given below for the Christoffel symbols ?_ij^k of a Levi-Civita connection in terms of partial derivatives of the associated metric tensor g_ij. ?_ij^k = (1/2) g^kl {?_i g_lj ? ?_l g_ij + ?_j g_il }. Problem 2. Compute the Christoffel symbols of the Levi-Civita connection associated to ea