Out[18]:
\[\newcommand{\Bold}[1]{\mathbf{#1}}\begin{array}{lcl} \mathrm{Riem}\left(g\right)_{ \phantom{\, {\eta}} \, {\chi} \, {\eta} \, {\chi} }^{ \, {\eta} \phantom{\, {\chi}} \phantom{\, {\eta}} \phantom{\, {\chi}} } & = & -\frac{1}{\cos\left({\eta}\right) + 1} \\ \mathrm{Riem}\left(g\right)_{ \phantom{\, {\eta}} \, {\theta} \, {\eta} \, {\theta} }^{ \, {\eta} \phantom{\, {\theta}} \phantom{\, {\eta}} \phantom{\, {\theta}} } & = & \frac{\cos\left({\eta}\right)^{2} \sin\left({\chi}\right)^{2} + 2 \, \cos\left({\eta}\right) \sin\left({\chi}\right)^{2} + \sin\left({\chi}\right)^{2}}{{\left(\cos\left({\eta}\right) + 3\right)} \sin\left({\eta}\right)^{2} - 4 \, \cos\left({\eta}\right) - 4} \\ \mathrm{Riem}\left(g\right)_{ \phantom{\, {\eta}} \, {\varphi} \, {\eta} \, {\varphi} }^{ \, {\eta} \phantom{\, {\varphi}} \phantom{\, {\eta}} \phantom{\, {\varphi}} } & = & \frac{{\left(\cos\left({\eta}\right)^{2} \sin\left({\chi}\right)^{2} + 2 \, \cos\left({\eta}\right) \sin\left({\chi}\right)^{2} + \sin\left({\chi}\right)^{2}\right)} \sin\left({\theta}\right)^{2}}{{\left(\cos\left({\eta}\right) + 3\right)} \sin\left({\eta}\right)^{2} - 4 \, \cos\left({\eta}\right) - 4} \\ \mathrm{Riem}\left(g\right)_{ \phantom{\, {\chi}} \, {\eta} \, {\eta} \, {\chi} }^{ \, {\chi} \phantom{\, {\eta}} \phantom{\, {\eta}} \phantom{\, {\chi}} } & = & -\frac{1}{\cos\left({\eta}\right) + 1} \\ \mathrm{Riem}\left(g\right)_{ \phantom{\, {\chi}} \, {\theta} \, {\chi} \, {\theta} }^{ \, {\chi} \phantom{\, {\theta}} \phantom{\, {\chi}} \phantom{\, {\theta}} } & = & \frac{2 \, \sin\left({\chi}\right)^{2}}{\cos\left({\eta}\right) + 1} \\ \mathrm{Riem}\left(g\right)_{ \phantom{\, {\chi}} \, {\varphi} \, {\chi} \, {\varphi} }^{ \, {\chi} \phantom{\, {\varphi}} \phantom{\, {\chi}} \phantom{\, {\varphi}} } & = & \frac{2 \, \sin\left({\chi}\right)^{2} \sin\left({\theta}\right)^{2}}{\cos\left({\eta}\right) + 1} \\ \mathrm{Riem}\left(g\right)_{ \phantom{\, {\theta}} \, {\eta} \, {\eta} \, {\theta} }^{ \, {\theta} \phantom{\, {\eta}} \phantom{\, {\eta}} \phantom{\, {\theta}} } & = & \frac{\cos\left({\eta}\right)^{5} + 5 \, \cos\left({\eta}\right)^{4} + 10 \, \cos\left({\eta}\right)^{3} + 10 \, \cos\left({\eta}\right)^{2} + 5 \, \cos\left({\eta}\right) + 1}{\sin\left({\eta}\right)^{6} - 6 \, {\left(\cos\left({\eta}\right) + 3\right)} \sin\left({\eta}\right)^{4} + 16 \, {\left(2 \, \cos\left({\eta}\right) + 3\right)} \sin\left({\eta}\right)^{2} - 32 \, \cos\left({\eta}\right) - 32} \\ \mathrm{Riem}\left(g\right)_{ \phantom{\, {\theta}} \, {\chi} \, {\chi} \, {\theta} }^{ \, {\theta} \phantom{\, {\chi}} \phantom{\, {\chi}} \phantom{\, {\theta}} } & = & \frac{2 \, {\left(\cos\left({\eta}\right) + 1\right)}}{\sin\left({\eta}\right)^{2} - 2 \, \cos\left({\eta}\right) - 2} \\ \mathrm{Riem}\left(g\right)_{ \phantom{\, {\theta}} \, {\varphi} \, {\theta} \, {\varphi} }^{ \, {\theta} \phantom{\, {\varphi}} \phantom{\, {\theta}} \phantom{\, {\varphi}} } & = & -\frac{2 \, {\left(\cos\left({\eta}\right) \sin\left({\chi}\right)^{2} + \sin\left({\chi}\right)^{2}\right)} \sin\left({\theta}\right)^{2}}{\sin\left({\eta}\right)^{2} - 2 \, \cos\left({\eta}\right) - 2} \\ \mathrm{Riem}\left(g\right)_{ \phantom{\, {\varphi}} \, {\eta} \, {\eta} \, {\varphi} }^{ \, {\varphi} \phantom{\, {\eta}} \phantom{\, {\eta}} \phantom{\, {\varphi}} } & = & \frac{\cos\left({\eta}\right)^{5} + 5 \, \cos\left({\eta}\right)^{4} + 10 \, \cos\left({\eta}\right)^{3} + 10 \, \cos\left({\eta}\right)^{2} + 5 \, \cos\left({\eta}\right) + 1}{\sin\left({\eta}\right)^{6} - 6 \, {\left(\cos\left({\eta}\right) + 3\right)} \sin\left({\eta}\right)^{4} + 16 \, {\left(2 \, \cos\left({\eta}\right) + 3\right)} \sin\left({\eta}\right)^{2} - 32 \, \cos\left({\eta}\right) - 32} \\ \mathrm{Riem}\left(g\right)_{ \phantom{\, {\varphi}} \, {\chi} \, {\chi} \, {\varphi} }^{ \, {\varphi} \phantom{\, {\chi}} \phantom{\, {\chi}} \phantom{\, {\varphi}} } & = & \frac{2 \, {\left(\cos\left({\eta}\right) + 1\right)}}{\sin\left({\eta}\right)^{2} - 2 \, \cos\left({\eta}\right) - 2} \\ \mathrm{Riem}\left(g\right)_{ \phantom{\, {\varphi}} \, {\theta} \, {\theta} \, {\varphi} }^{ \, {\varphi} \phantom{\, {\theta}} \phantom{\, {\theta}} \phantom{\, {\varphi}} } & = & \frac{2 \, {\left(\cos\left({\eta}\right) \sin\left({\chi}\right)^{2} + \sin\left({\chi}\right)^{2}\right)}}{\sin\left({\eta}\right)^{2} - 2 \, \cos\left({\eta}\right) - 2} \end{array}\]