From Frenet to Cartan : the method of moving frames / Jeanne N. Clelland

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Graduate Studies in Mathematics ; v.178Publisher: Providence : American Mathematical Society, 2017Description: 1 Online-Ressource (433 p)Subject(s): Additional physical formats: 1470429527 | 9781470429522 | 1470437473. | 9781470437473. | Erscheint auch als: From Frenet to Cartan. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2017. xvi, 414 Seiten | Print version: From Frenet to Cartan: The Method of Moving Frames. Providence : American Mathematical Society,c2017DDC classification:
  • 515.63
MSC: MSC: *53-02 | 53A04 | 53C30 | 58A15 | 58J72 | 53B25 | 53A05 | 53A07RVK: RVK: SK 340 | SK 370LOC classification:
  • QA433.C564 2017eb
Online resources: Summary: 8.4. Maple computationsChapter 9. Pseudospherical surfaces and Bäcklund's theorem; 9.1. Introduction; 9.2. Line congruences; 9.3. Bäcklund's theorem; 9.4. Pseudospherical surfaces and the sine-Gordon equation; 9.5. The Bäcklund transformation for the sine-Gordon equation; 9.6. Maple computations; Chapter 10. Two classical theorems; 10.1. Doubly ruled surfaces in \R³; 10.2. The Cauchy-Crofton formula; 10.3. Maple computations; Part 4 . Beyond the flat case: Moving frames on Riemannian manifolds; Chapter 11. Curves and surfaces in elliptic and hyperbolic spaces; 11.1. IntroductionSummary: Chapter 6. Curves and surfaces in equi-affine space6.1. Introduction; 6.2. Moving frames for curves in \bb{ }³; 6.3. Moving frames for surfaces in \bb{ }³; 6.4. Maple computations; Chapter 7. Curves and surfaces in projective space; 7.1. Introduction; 7.2. Moving frames for curves in \bb{ }²; 7.3. Moving frames for curves in \bb{ }³; 7.4. Moving frames for surfaces in \bb{ }³; 7.5. Maple computations; Part 3 . Applications of moving frames; Chapter 8. Minimal surfaces in \E³ and \bb{ }³; 8.1. Introduction; 8.2. Minimal surfaces in \bb{ }³; 8.3. Minimal surfaces in \bb{ }³Summary: The method of moving frames originated in the early nineteenth century with the notion of the Frenet frame along a curve in Euclidean space. Later, Darboux expanded this idea to the study of surfaces. The method was brought to its full power in the early twentieth century by Elie Cartan, and its development continues today with the work of Fels, Olver, and others. This book is an introduction to the method of moving frames as developed by Cartan, at a level suitable for beginning graduate students familiar with the geometry of curves and surfaces in Euclidean space. The main focus is on the usPPN: PPN: 898057876Package identifier: Produktsigel: ZDB-4-NLEBK
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