Differential Forms and Applications

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Beschreibung


Dieses Buch vom M. do Carmo, Träger des Mathematikpreises 1992 der "Third World Academy of Sciences", gibt eine Einführung in die Theorie differenzierbarer Formen. Da es nur Grundkenntnisse in Differential- und Integralrechnung sowie linearer Algebra voraussetzt, eignet es sich als Lehrbuch für Mathematik- und Physikstudenten im 4.- 6. Semester.

The book treats differential forms and uses them to study some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will makethem attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely the Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames of E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. Everything is then put together in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.

Klappentext

An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.



Zusammenfassung

M.P. Do Carmo

Differential Forms and Applications

"This book treats differential forms and uses them to study some local and global aspects of differential geometry of surfaces. Each chapter is followed by interesting exercises. Thus, this is an ideal book for a one-semester course."-ACTA SCIENTIARUM MATHEMATICARUM



Inhalt

1. Differential Forms in Rn.- 2. Line Integrals.- 3. Differentiable Manifolds.- 4. Integration on Manifolds; Stokes Theorem and Poincare's Lemma.- 1. Integration of Differential Forms.- 2. Stokes Theorem.- 3. Poincare'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.

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Produktinformationen

Titel
Differential Forms and Applications
Untertitel
Universitext
Autor
EAN
9783540576181
ISBN
3540576185
Format
Kartonierter Einband
Herausgeber
Springer Berlin Heidelberg
Genre
Mathematik
Anzahl Seiten
136
Gewicht
219g
Größe
H235mm x B155mm x T7mm
Jahr
1998
Untertitel
Englisch
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