hearing-aid 发表于 2025-3-21 16:24:27

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使隔离 发表于 2025-3-21 21:11:54

Curvature,ng curvature is the central theme of Riemannian geometry. The idea of a Riemannian metric having curvature, while intuitively appealing and natural, is for most people the stumbling block for further progress into the realm of geometry.

不足的东西 发表于 2025-3-22 02:34:06

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粘连 发表于 2025-3-22 07:16:41

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CRAB 发表于 2025-3-22 09:11:01

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EXALT 发表于 2025-3-22 15:11:49

Sectional Curvature Comparison II, Gromoll. Next, we discuss Gromov’s finiteness theorem for bounds on Betti numbers and generators for the fundamental group Finally, we show that these techniques can be adapted to prove the Grove-Petersen homotopy finiteness theorem.

谄媚于人 发表于 2025-3-22 17:35:55

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黑豹 发表于 2025-3-22 23:50:20

Curvature,confine ourselves to infinitesimal considerations. The most important and often also least understood object of Riemannian geometry is that of the Riemannian connection. From this concept it will be possible to define curvature and more familiar items like gradients and Hessians of functions. Studyi

煞费苦心 发表于 2025-3-23 03:11:36

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表主动 发表于 2025-3-23 06:01:17

Hypersurfaces,nvex im­mersions are embeddings of spheres. We then establish a connection between convexity and positivity of the intrinsic curvatures. This connection will enable us to see that ℂ.. and the Berger spheres are not even locally hypersurfaces in Euclidean space. We give a brief description of some cl
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查看完整版本: Titlebook: Riemannian Geometry; Peter Petersen Textbook 19981st edition Springer Science+Business Media New York 1998 Riemannian geometry.Spinor.Tens