拖累 发表于 2025-3-21 16:20:30
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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. embitinerary 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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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 ticulinfinite 发表于 2025-3-22 18:02:15
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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 2191-6675GENUS 发表于 2025-3-23 04:44:57
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https://doi.org/10.1007/978-3-662-03118-6Harmonische Abbildungen; Hodge theorem; Levi-Civita connection; Lovi-Civita-Zusammenhang; Minimalflächen