Another demo here at MWC showed how you could make the Robot Phone "sleep" by covering its gimbal eye, though it's odd that the camera is still exposed rather than folded away. My main concern with the Robot Phone is the robustness and durability of its robotic mechanisms. We've lived through several waves of smartphones that attempted much simpler mechanical camera functions and the threat of dust or heavy-handed users can't be ignored.
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For the Poincaré half-space model in dimension 2, the metric evaluates on the coordinate tangent vectors \(\frac{\partial}{\partial x}, \frac{\partial}{\partial y} \in T_pM\) as \[g_p\!\left(\frac{\partial}{\partial x^i}\bigg|_p,\;\frac{\partial}{\partial x^j}\bigg|_p\right) = \frac{1}{y^2}\,\delta_{ij},\] i.e. the coordinate tangent vectors are orthogonal and each has length \(\frac{1}{y}\) — shrinking to zero as \(p\) approaches the boundary \(y\to 0\), which is what makes the space “infinitely large” near the boundary.，推荐阅读safew官方版本下载获取更多信息