Titlebook: Differential Manifolds; Serge Lang Textbook 19852nd edition Springer-Verlag New York Inc. 1985 Immersion.Submersion.Tensor.Volume.differen

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The Irrelevance of J.K. Rowlingormal definition. We then make manifolds into a category, and discuss special types of morphisms. We define the tangent space at each point, and apply the criteria following the inverse function theorem to get a local splitting of a manifold when the tangent space splits at a point.

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https://doi.org/10.1057/9781137473349In our discussion of vector bundles, we put no greater structure on the fibers than that of topological vector space (of the same category as those used to build up manifolds). One can strengthen the notion so as to include the metric structure, and we are thus led to consider Hilbert bundles, whose fibers are Hilbert spaces.

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Riemannian Metrics,In our discussion of vector bundles, we put no greater structure on the fibers than that of topological vector space (of the same category as those used to build up manifolds). One can strengthen the notion so as to include the metric structure, and we are thus led to consider Hilbert bundles, whose fibers are Hilbert spaces.

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,Stokes’ Theorem,If . is a manifold and . a submanifold, then any differential form on . induces a form on .. We can view this as a very special case of the inverse image of a form, under the embedding (injection) map

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Manifolds,ormal definition. We then make manifolds into a category, and discuss special types of morphisms. We define the tangent space at each point, and apply the criteria following the inverse function theorem to get a local splitting of a manifold when the tangent space splits at a point.

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Differential Calculus,my . give a self-contained and complete treatment for Banach spaces. We summarize certain facts concerning their properties as topological vector spaces, and then we summarize differential calculus. . and start immediately with Chapter II if he is accustomed to thinking about the derivative of a map