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Titlebook: Differentiable Manifolds; Forms, Currents, Har Georges Rham Book 1984 Springer-Verlag Berlin Heidelberg 1984 Differenzierbare Mannigfaltigk

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書目名稱Differentiable Manifolds
副標(biāo)題Forms, Currents, Har
編輯Georges Rham
視頻videohttp://file.papertrans.cn/279/278629/278629.mp4
叢書名稱Grundlehren der mathematischen Wissenschaften
圖書封面Titlebook: Differentiable Manifolds; Forms, Currents, Har Georges Rham Book 1984 Springer-Verlag Berlin Heidelberg 1984 Differenzierbare Mannigfaltigk
描述In this work, I have attempted to give a coherent exposition of the theory of differential forms on a manifold and harmonic forms on a Riemannian space. The concept of a current, a notion so general that it includes as special cases both differential forms and chains, is the key to understanding how the homology properties of a manifold are immediately evident in the study of differential forms and of chains. The notion of distribution, introduced by L. Schwartz, motivated the precise definition adopted here. In our terminology, distributions are currents of degree zero, and a current can be considered as a differential form for which the coefficients are distributions. The works of L. Schwartz, in particular his beautiful book on the Theory of Distributions, have been a very great asset in the elaboration of this work. The reader however will not need to be familiar with these. Leaving aside the applications of the theory, I have restricted myself to considering theorems which to me seem essential and I have tried to present simple and complete of these, accessible to each reader having a minimum of mathematical proofs background. Outside of topics contained in all degree programs
出版日期Book 1984
關(guān)鍵詞Differenzierbare Mannigfaltigkeit; Rham; Riemannian manifold; Varieties; manifold
版次1
doihttps://doi.org/10.1007/978-3-642-61752-2
isbn_softcover978-3-642-61754-6
isbn_ebook978-3-642-61752-2Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 1984
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0072-7830 nnian space. The concept of a current, a notion so general that it includes as special cases both differential forms and chains, is the key to understanding how the homology properties of a manifold are immediately evident in the study of differential forms and of chains. The notion of distribution,
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Supervisory Control of Software Systems a sequence of C. forms with supports all contained in a single compact set which is in the interior of the domain of a local coordinate system .,…, . such that each derivative of each coefficient of the form . (represented using .,…, .. tends uniformly to zero as .→∞, then . [.]→0..
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Book 1984e. The concept of a current, a notion so general that it includes as special cases both differential forms and chains, is the key to understanding how the homology properties of a manifold are immediately evident in the study of differential forms and of chains. The notion of distribution, introduce
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Currents, a sequence of C. forms with supports all contained in a single compact set which is in the interior of the domain of a local coordinate system .,…, . such that each derivative of each coefficient of the form . (represented using .,…, .. tends uniformly to zero as .→∞, then . [.]→0..
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Differential Forms,ng this in terms of the local coordinates .,.,., the above differential form reduces to the expression .If we change the local coordinate system, the coefficients . transform as the components of a covector.
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