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\end{cases}Tc(x)=⎩⎨⎧0−0.827429x+0.089718x(lnx−1)+829.418770−0.328481x+0.043109x(lnx−1)−1248.2661210.051162x+0.010441x(lnx−1)−4888.819148235484.5479+0.1862(x−1265000)if x
Poincaré half-space model. Take the open upper half-space \[\mathbb{H}^n := \{(x_1,\dots,x_n)\in\mathbb{R}^n \mid x_n 0\}\] equipped with the Riemannian metric whose components on the coordinate tangent vectors are \[g_{ij}(p) \;=\; g_p\!\left(\frac{\partial}{\partial x_i}\bigg|_p,\; \frac{\partial}{\partial x_j}\bigg|_p\right) \;=\; \frac{1}{p_n^2}\,\delta_{ij}.\] Geodesics are semicircles (or rays) orthogonal to the boundary hyperplane \(\{x_n = 0\}\).