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;
家门口的集市对冬来说像捡到了宝，去县乡他最爱逛当地集市。来矿区之前，他就说，到那边做各种好吃的。到现在还没见怎么做，倒是图方便买了不少现成的：海鲜、卤肉、烧饼、炒栗子……回来自己倒杯威士忌，吃得挺美。海鲜买自海鲜基地，叫基地，其实就一个门脸。矿区地方小，没多少人吃海鲜，我一般不进门，冬进去买。我做惯了甩手掌柜。如果不是冬，好多东西我都不知道会不会去吃，比如大闸蟹。听上去，我穷得可以，倒确实也没富过，其实主要是怕麻烦。母蟹肚子是完整的白壳，公蟹肚子上像有口钟，或是塔。意思是，要想横着走，必得当个托塔天王，还得坐如钟。我第一次吃蚕蛹，也是冬买的。我很长时间都对牛奶不耐受，小时候没喝过，到了高中，第一次喝酸奶。小汽车也是高中第一次坐，连车门也不会开，教我开车门的是个小屁孩儿。记忆中不少这种鸡零狗碎的事。
，更多细节参见体育直播
Wöchentliche Ausgabe des SPIEGEL als E-Paper
架空商品を架空注文して架空決済され架空配達に回されて買い物気分だけ味わえる通販サイト「カウカウ」