Heel opens in theaters and on demand on March 6.
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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They may have used a chatbot while arriving at that belief, which is fine. But their chatbot interaction was helpful to them in a context, and pasting from it doesn’t reliably bring me there.
苹果似乎提前在官网监管信息页面中泄露了其传闻已久的全新低价 MacBook 产品名称——“MacBook Neo”。这款机型预计将于本周三正式发布。
Skyward Wildfire has a bold plan to prevent wildfires: stop the lightning that causes them. The Vancouver-based startup raised $5.7 million claiming it can prevent lightning strikes using cloud seeding with aluminum-coated glass fibers—the same military chaff used to jam radar systems.