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

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發(fā)表于 2025-3-21 18:40:51 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Differential Manifolds
編輯Serge Lang
視頻videohttp://file.papertrans.cn/279/278781/278781.mp4
圖書(shū)封面Titlebook: Differential Manifolds;  Serge Lang Textbook 19852nd edition Springer-Verlag New York Inc. 1985 Immersion.Submersion.Tensor.Volume.differen
描述The present volume supersedes my Introduction to Differentiable Manifolds written a few years back. I have expanded the book considerably, including things like the Lie derivative, and especially the basic integration theory of differential forms, with Stokes‘ theorem and its various special formulations in different contexts. The foreword which I wrote in the earlier book is still quite valid and needs only slight extension here. Between advanced calculus and the three great differential theories (differential topology, differential geometry, ordinary differential equations), there lies a no-man‘s-land for which there exists no systematic exposition in the literature. It is the purpose of this book to fill the gap. The three differential theories are by no means independent of each other, but proceed according to their own flavor. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.). One may also use differentiable structures on topological manifolds to determine the topological structure of the manifold (e.g. it la Smale [26]).
出版日期Textbook 19852nd edition
關(guān)鍵詞Immersion; Submersion; Tensor; Volume; differential geometry; differential topology; differenzierbare Mann
版次2
doihttps://doi.org/10.1007/978-1-4684-0265-0
isbn_softcover978-0-387-96113-2
isbn_ebook978-1-4684-0265-0
copyrightSpringer-Verlag New York Inc. 1985
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沙發(fā)
發(fā)表于 2025-3-22 00:03:47 | 只看該作者
Voicing Lyric: The Songs of Mary Wrothes of our rectangles very slightly (an ε/2. argument). We shall prove here some criteria for a set to have measure 0. We leave it to the reader to verify that instead of rectangles, we could have used cubes in our characterization of a set of a measure 0 (a cube being a rectangle all of whose sides have the same length).
板凳
發(fā)表于 2025-3-22 03:52:45 | 只看該作者
Integration of Differential Forms,es of our rectangles very slightly (an ε/2. argument). We shall prove here some criteria for a set to have measure 0. We leave it to the reader to verify that instead of rectangles, we could have used cubes in our characterization of a set of a measure 0 (a cube being a rectangle all of whose sides have the same length).
地板
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https://doi.org/10.1057/9780230279711em surrounding such forms. In order to have at least one application, we discuss the fundamental 2-form, and in the next chapter connect it with Riemannian metrics in order to construct canonically the spray associated with such a metric.
7#
發(fā)表于 2025-3-22 20:07:42 | 只看該作者
https://doi.org/10.1057/9780230279711tion in terms of differential forms, for which the reader needs to know the local definition of the exterior derivative. However, the condition involving differential forms is proved to be equivalent to the vector field condition at the very beginning, and does not reappear explicitly afterwards.
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發(fā)表于 2025-3-23 00:08:01 | 只看該作者
Differential Calculus, as a linear transformation. (In the finite dimensional case, when bases have been selected, the entries in the matrix of this transformation are the partial derivatives of the map.) We have repeated the proofs for the more important theorems, for the ease of the reader.
9#
發(fā)表于 2025-3-23 03:18:40 | 只看該作者
Vector Bundles,In the chapters on differential forms and Riemannian metrics, we shall discuss in greater detail the constructions associated with multilinear alternating forms, and symmetric positive definite forms.
10#
發(fā)表于 2025-3-23 07:25:11 | 只看該作者
Operations on Vector Fields and Differential Forms,em surrounding such forms. In order to have at least one application, we discuss the fundamental 2-form, and in the next chapter connect it with Riemannian metrics in order to construct canonically the spray associated with such a metric.
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