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[求助]
為什么一時(shí)說黎曼幾何是非歐幾何,一時(shí)又說黎曼幾何是微分幾何 已有5人參與
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有時(shí)候看到黎曼幾何是非歐幾何的一種,,一時(shí)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 |
專家顧問 (職業(yè)作家)
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專家經(jīng)驗(yàn): +362 |
| 據(jù)龔升的說法,非歐幾何是第5公設(shè)(過已知直線外一點(diǎn),能且只能作一條直線與已知直線平行)不成立的幾何。黎曼在非歐幾何的思想基礎(chǔ)上發(fā)展了更廣泛的黎曼幾何。 |

專家顧問 (著名寫手)
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專家經(jīng)驗(yàn): +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. |

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