Differentiable Manifolds: Forms, Currents, Harmonic Forms (Grundlehren der mathematischen Wissenschaften)

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9783642617546: Differentiable Manifolds: Forms, Currents, Harmonic Forms (Grundlehren der mathematischen Wissenschaften)

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, the knowledge of the most elementary notions of general topology and tensor calculus and also, for the final chapter, that of the Fredholm theorem, would in principle be adequate.

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1.

Georges de Rham (author), F.R. Smith (translator), S.S. Chern (introduction)
Editorial: Springer Berlin Heidelberg 2011-10-12, Berlin, Heidelberg (2011)
ISBN 10: 3642617549 ISBN 13: 9783642617546
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Descripción Springer Berlin Heidelberg 2011-10-12, Berlin, Heidelberg, 2011. paperback. Estado de conservación: New. Nº de ref. de la librería 9783642617546

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Rham, Georges de / Chern, S. S.
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Descripción Estado de conservación: New. Publisher/Verlag: Springer, Berlin | Forms, Currents, Harmonic Forms | 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, the knowledge of the most elementary notions of general topology and tensor calculus and also, for the final chapter, that of the Fredholm theorem, would in principle be adequate. | I. Notions About Manifolds.-1. The Notion of a Manifold and a Differentiable Structure.-2. Partition of Unity. Functions on Product Spaces.-3. Maps and Imbeddings of Manifolds.- II. Differential Forms.-4. Differential Forms of Even Type.-5. Differential Forms of Odd Type. Orientation of Manifolds and Maps.-6. Chains. Stokes' Formula.-7. Double Forms.- III. Currents.-8. Definition of Currents.-9. The Vector Spaces E, D, Ep, and Dp.-10. The Vector Spaces D , E , D p, and E p.-11. Boundary of a Current. Image of a Current by a Map.-12. Double Currents.-13. Transformations of Double Forms and Currents by a Map.-14. Homotopy Formulas.-15. Regularization.-16. Operators Associated with a Double Current.-17. Reflexitivity of E and D. Regular Operators and Regularizing Operators.- IV. Homologies.-18. Homology Groups.-19. Homologies in IRn.-20. The Kronecker Index.-21. Homologies Between Forms and Chains in a Manifold Endowed with a Polyhedral Subdivision.-22. Duality in a Manifold Endowed with a Polyhedral Subdivision.-23. Duality in Any Differentiable Manifold.- V. Harmonic Forms.-24. Riemannian Spaces. Adjoint Form.-25. The Metric Transpose of an Operator. The Operators ? and ?.-26. Expressions of the Operators d, ?, and ? Using Covariant Derivatives.-27. Properties of the Geodesic Distance.-28. The Parametrix.-29. The Regularity of Harmonic Currents.-30. The Local Study of the Equation ??= ? Elementary Kernels.-31. The Equation ?S = T on a Compact Space. The Operators H and G.-32. The Decomposition Formula in a Non-Compact Space.-33. Explicit Formula for the Kronecker Index.-34. The Analyticity of Harmonic Forms.-35. Square Summable Harmonic Forms on a Complete Riemannian Space.- List of Notation. | Format: Paperback | Language/Sprache: english | 288 gr | 235x155x9 mm | 170 pp. Nº de ref. de la librería K9783642617546

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Geroges De Rham
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Descripción Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, 2011. PAP. Estado de conservación: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería LQ-9783642617546

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Rham, Georges De
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Descripción Springer, 2016. Paperback. Estado de conservación: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Nº de ref. de la librería ria9783642617546_lsuk

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GEORGES DE RHAM
Editorial: Springer (2011)
ISBN 10: 3642617549 ISBN 13: 9783642617546
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Descripción Springer, 2011. Paperback. Estado de conservación: NEW. 9783642617546 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0362373

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Georges de Rham
Editorial: Springer Okt 2011 (2011)
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Descripción Springer Okt 2011, 2011. Taschenbuch. Estado de conservación: Neu. Neuware - 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, the knowledge of the most elementary notions of general topology and tensor calculus and also, for the final chapter, that of the Fredholm theorem, would in principle be adequate. 184 pp. Englisch. Nº de ref. de la librería 9783642617546

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Georges de Rham
Editorial: Springer Okt 2011 (2011)
ISBN 10: 3642617549 ISBN 13: 9783642617546
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Agrios-Buch
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Descripción Springer Okt 2011, 2011. Taschenbuch. Estado de conservación: Neu. Neuware - 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, the knowledge of the most elementary notions of general topology and tensor calculus and also, for the final chapter, that of the Fredholm theorem, would in principle be adequate. 184 pp. Englisch. Nº de ref. de la librería 9783642617546

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Geroges De Rham
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ISBN 10: 3642617549 ISBN 13: 9783642617546
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Descripción Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, 2011. PAP. Estado de conservación: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IQ-9783642617546

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Georges de Rham
Editorial: Springer Okt 2011 (2011)
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Descripción Springer Okt 2011, 2011. Taschenbuch. Estado de conservación: Neu. This item is printed on demand - Print on Demand Neuware - 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, the knowledge of the most elementary notions of general topology and tensor calculus and also, for the final chapter, that of the Fredholm theorem, would in principle be adequate. 184 pp. Englisch. Nº de ref. de la librería 9783642617546

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Rham, Georges de
Editorial: Springer (2017)
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Descripción Springer, 2017. Paperback. Estado de conservación: New. Never used! This item is printed on demand. Nº de ref. de la librería 3642617549

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