Problem
Problem 6.75 Consider on $\mathbb{R}^{3}$ the metric
$$
g=\mathrm{e}^{2 z}\left(\mathrm{~d} x^{2}+\mathrm{d} y^{2}+\mathrm{d} z^{2}\right)
$$
Compute $R\left(\frac{\partial}{\partial x}, \frac{\partial}{\partial z}, \frac{\partial}{\partial x}, \frac{\partial}{\partial z}\right)$, where $R$ denotes the Riemann-Christoffel curvature tensor.