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[求助]
為什么一時說黎曼幾何是非歐幾何,一時又說黎曼幾何是微分幾何 已有5人參與
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有時候看到黎曼幾何是非歐幾何的一種,,一時又說黎曼幾何是微分幾何的分支,求解答 發(fā)自小木蟲Android客戶端 |
銀蟲 (正式寫手)
專家顧問 (著名寫手)
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專家經(jīng)驗: +342 |
| Riemannian geometry is a global differential geometry. Locally we can define local coordinates and treat it as Euclidean space. We can define inner product, metric and angle etc. Differential geometry is opposite to integral geometry. When we talk about smoothness, we want to do differential. Thus Riemannian geometry is one kind of differential geometry since we need differential to calculate normal vector, tangent vector, and of course curvatures. There are many kinds of metric you can define locally. If it's Riemannian metric, you get Riemannian geometry. If you define other kinds of metric, you get other kinds of differential geometry. |

專家顧問 (職業(yè)作家)
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專家經(jīng)驗: +362 |

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