Differential Forms and Applications
This is a free translation of a set of notes published originally in Portuguese in 1971. They were translated for a course in the College of Differential Geome try, ICTP, Trieste, 1989. In the English translation we omitted a chapter on the Frobenius theorem and an appendix on the nonexistence of a...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1994, 1994
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| Edition: | 1st ed. 1994 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Differential Forms in Rn
- 2. Line Integrals
- 3. Differentiable Manifolds
- 4. Integration on Manifolds; Stokes Theorem and Poincaré’s Lemma
- 1. Integration of Differential Forms
- 2. Stokes Theorem
- 3. Poincaré’s Lemma
- 5. Differential Geometry of Surfaces
- 1. The Structure Equations of Rn
- 2. Surfaces in R3
- 3. Intrinsic Geometry of Surfaces
- 6. The Theorem of Gauss-Bonnet and the Theorem of Morse
- 1. The Theorem of Gauss-Bonnet
- 2. The Theorem of Morse
- References