A Riemannian metric on a smooth manifold \(M\) is a family of inner products \[g_p : T_pM \times T_pM \;\longrightarrow\; \mathbb{R}, \qquad p \in M,\] varying smoothly in \(p\), such that each \(g_p\) is symmetric and positive-definite. In local coordinates the metric is completely determined by its values on basis tangent vectors: \[g_{ij}(p) \;:=\; g_p\!\left(\frac{\partial}{\partial x^i}\bigg|_p,\; \frac{\partial}{\partial x^j}\bigg|_p\right), \qquad g_{ij} = g_{ji},\] with the matrix \((g_{ij}(p))\) positive-definite at every point. The length of a tangent vector \(v = \sum_i v^i \frac{\partial}{\partial x^i}\in T_pM\) is then \(\|v\|_g = \sqrt{\sum_{i,j} g_{ij}(p)\, v^i v^j}\).
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“不繁”，强调制度的简洁可行，突出针对性和指导性。“不繁”之要，是以必要的规则，达致有效、严密的约束。若条文冗长空洞、脱离实践，非但不能发挥制度的规范作用，还会因难以把握、让执行者无所适从而损害制度威信。习近平总书记强调“不管建立和完善什么制度，都要本着于法周延、于事简便的原则”，指出了“密而不繁”的主要内涵。其中，于法周延的核心在“密”，织密制度之网，实现系统集成、协同高效；于事简便的关键在“简”，剔除冗余繁琐，确保制度立得住、行得通、真管用。