Author | Rham, Georges de. author |
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Title | Differentiable Manifolds [electronic resource] : Forms, Currents, Harmonic Forms / by Georges de Rham |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1984 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61752-2 |
Descript | X, 170 p. online resource |
I. Notions About Manifolds -- ยง1. The Notion of a Manifold and a Differentiable Structure -- ยง2. Partition of Unity. Functions on Product Spaces -- ยง3. Maps and Imbeddings of Manifolds -- II. Differential Forms -- ยง4. Differential Forms of Even Type -- ยง5. Differential Forms of Odd Type. Orientation of Manifolds and Maps -- ยง6. Chains. Stokesโ Formula -- ยง7. Double Forms -- III. Currents -- ยง8. Definition of Currents -- ยง9. The Vector Spaces E, D, Ep, and Dp -- ยง10. The Vector Spaces Dยด, Eยด, Dยดp, and Eยดp -- ยง11. Boundary of a Current. Image of a Current by a Map -- ยง12. Double Currents -- ยง13. Transformations of Double Forms and Currents by a Map -- ยง14. Homotopy Formulas -- ยง15. Regularization -- ยง16. Operators Associated with a Double Current -- ยง17. Reflexitivity of E and D. Regular Operators and Regularizing Operators -- IV. Homologies -- ยง18. Homology Groups -- ยง19. Homologies in IRn -- ยง20. The Kronecker Index -- ยง21. Homologies Between Forms and Chains in a Manifold Endowed with a Polyhedral Subdivision -- ยง22. Duality in a Manifold Endowed with a Polyhedral Subdivision -- ยง23. Duality in Any Differentiable Manifold -- V. Harmonic Forms -- ยง24. Riemannian Spaces. Adjoint Form -- ยง25. The Metric Transpose of an Operator. The Operators ? and ? -- ยง26. Expressions of the Operators d, ?, and ? Using Covariant Derivatives -- ยง27. Properties of the Geodesic Distance -- ยง28. The Parametrix -- ยง29. The Regularity of Harmonic Currents -- ยง30. The Local Study of the Equation ??= ?. Elementary Kernels -- ยง31. The Equation ?S = T on a Compact Space. The Operators H and G -- ยง32. The Decomposition Formula in a Non-Compact Space -- ยง33. Explicit Formula for the Kronecker Index -- ยง34. The Analyticity of Harmonic Forms -- ยง35. Square Summable Harmonic Forms on a Complete Riemannian Space -- List of Notation