Often people write these metrics as \(ds^2 = \sum_{i,j} g_{ij}\,dx^i\,dx^j\), where each \(dx^i\) is a covector (1-form), i.e. an element of the dual space \(T_p^*M\). For finite dimensional vectorspaces there is a canonical isomorphism between them and their dual: given the coordinate basis \(\bigl\{\frac{\partial}{\partial x^1},\dots,\frac{\partial}{\partial x^n}\bigr\}\) of \(T_pM\), there is a unique dual basis \(\{dx^1,\dots,dx^n\}\) of \(T_p^*M\) defined by \[dx^i\!\left(\frac{\partial}{\partial x^j}\right) = \delta^i{}_j.\] This extends to isomorphisms \(T_pM \to T_p^*M\). Under this identification, the bilinear form \(g_p\) on \(T_pM \times T_pM\) is represented by the symmetric tensor \(\sum_{i,j} g_{ij}\,dx^i \otimes dx^j\) acting on pairs of tangent vectors via \[\left(\sum_{i,j} g_{ij}\,dx^i\otimes dx^j\right)\!\!\left(\frac{\partial}{\partial x^k},\frac{\partial}{\partial x^l}\right) = g_{kl},\] which recovers exactly the inner products \(g_p\!\left(\frac{\partial}{\partial x^k},\frac{\partial}{\partial x^l}\right)\) from before. So both descriptions carry identical information;
Does paying guarantee attention from everyone you message? Of course not. The usual dating-app dynamics still apply — heterosexual men, for instance, should expect to work harder for responses than heterosexual women. Being attractive, fit, or witty helps, and being all three helps even more.
，这一点在同城约会中也有详细论述
这就意味着，对于绝大多数缺乏结构化表达能力的下沉市场受众而言，就算把最先进的 AI 摆在他们面前，吸引力也还是不如短视频里的黑丝和大腿。他们无法从这种高认知门槛的交互中获得多巴胺，自然也就不具备分辨 AI 生成内容的能力。
const hookedSet = function (v) {
Protesters scatter, ducking into the gaps between buildings and pavement. Some simply cover their heads for protection. Yogendra Nyaupane, 24, is hit and fatally wounded.