Denial 发表于 2025-3-21 16:27:04

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dry-eye 发表于 2025-3-21 23:25:52

Review of Tensors, Manifolds, and Vector Bundles,reviewing the basic definitions and properties of tensors on a finite-dimensional vector space. When we put together spaces of tensors on a manifold, we obtain a particularly useful type of geometric structure called a “vector bundle,” which plays an important role in many of our investigations. Bec

EPT 发表于 2025-3-22 04:10:17

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Admire 发表于 2025-3-22 05:13:57

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Malfunction 发表于 2025-3-22 09:16:23

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绅士 发表于 2025-3-22 15:48:43

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性学院 发表于 2025-3-22 20:44:33

Curvature,ocally isometric, we are led to a definition of the Riemannian curvature tensor as a measure of the failure of second covariant derivatives to commute. Then we prove the main result of this chapter: A manifold has zero curvature if and only if it is flat, that is, locally isometric to Euclidean spac

夹克怕包裹 发表于 2025-3-23 00:43:17

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collagenase 发表于 2025-3-23 03:34:36

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Fretful 发表于 2025-3-23 07:22:00

Curvature and Topology, and topology. Before treating the topological theorems themselves, we prove some comparison theorems for manifolds whose curvature is bounded above. These comparisons are based on a simple ODE comparison theorem due to Sturm, and show that if the curvature is bounded above by a constant, then the m
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查看完整版本: Titlebook: Riemannian Manifolds; An Introduction to C John M. Lee Textbook 19971st edition Springer Science+Business Media New York 1997 Riemannian ge