拖累 发表于 2025-3-21 16:20:30

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移植 发表于 2025-3-21 21:05:58

Morse Theory and Closed Geodesics,metry, B. Riemann also expressed the idea that a manifold can be reconstructed from the level hypersurfaces of a continuous function. If the function is not only continuous, but also differentiable, all such hyper-surfaces that do not contain any critical points of the function are regular, i.e. emb

itinerary 发表于 2025-3-22 04:09:34

Geodesics and Jacobi Fields, defined tangent spaces at .. Thus, in a double point of .(.), the tangent space can be specified by specifying the preimage (. or .). This can be formalized as follows: We consider the bundle .*(.) over ., pulled back by .. The fiber over . ∈ . here is ....

Anticonvulsants 发表于 2025-3-22 05:19:28

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山崩 发表于 2025-3-22 09:27:50

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汇总 发表于 2025-3-22 16:26:32

0172-5939 geometric and analytic methods in the study of Riemannian manifolds. In the first chapter, we introduce the basic geometric concepts, like dif­ ferentiable manifolds, tangent spaces, vector bundles, vector fields and one­ parameter groups of diffeomorphisms, Lie algebras and groups and in par­ ticul

infinite 发表于 2025-3-22 18:02:15

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ODIUM 发表于 2025-3-22 22:50:31

0172-5939 heir results will be used in the remaining, more advanced chapters that are essentially independent of each other. In the fifth chapter, we develop Morse theory978-3-662-03118-6Series ISSN 0172-5939 Series E-ISSN 2191-6675

GENUS 发表于 2025-3-23 04:44:57

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Fatten 发表于 2025-3-23 08:37:44

https://doi.org/10.1007/978-3-662-03118-6Harmonische Abbildungen; Hodge theorem; Levi-Civita connection; Lovi-Civita-Zusammenhang; Minimalflächen
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查看完整版本: Titlebook: Riemannian Geometry and Geometric Analysis; Jürgen Jost Textbook 19951st edition Springer-Verlag Berlin Heidelberg 1995 Harmonische Abbild