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Cover: 9780387947327 | Differential Geometry | R. W. Sharpe | Buch | Englisch | 2000
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Differential Geometry
Cartan's Generalization of Klein's Erlangen Program
Buch von R. W. Sharpe
Sprache: Englisch

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Beschreibung
Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of "espaces généralisés" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.
Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of "espaces généralisés" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.
Inhaltsverzeichnis
In the Ashes of the Ether: Differential Topology.- Looking for the Forest in the Leaves: Folations.- The Fundamental Theorem of Calculus.- Shapes Fantastic: Klein Geometries.- Shapes High Fantastical: Cartan Geometries.- Riemannian Geometry.- Möbius Geometry.- Projective Geometry.- Appendix A - E.
Details
Erscheinungsjahr: 1997
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 452
Reihe: Graduate Texts in Mathematics
Inhalt: xx
426 S.
ISBN-13: 9780387947327
ISBN-10: 0387947329
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Sharpe, R. W.
Auflage: 1997
Hersteller: Springer US
Springer New York
Graduate Texts in Mathematics
Maße: 241 x 160 x 30 mm
Von/Mit: R. W. Sharpe
Erscheinungsdatum: 12.06.1997
Gewicht: 0,84 kg
preigu-id: 105102550
Inhaltsverzeichnis
In the Ashes of the Ether: Differential Topology.- Looking for the Forest in the Leaves: Folations.- The Fundamental Theorem of Calculus.- Shapes Fantastic: Klein Geometries.- Shapes High Fantastical: Cartan Geometries.- Riemannian Geometry.- Möbius Geometry.- Projective Geometry.- Appendix A - E.
Details
Erscheinungsjahr: 1997
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 452
Reihe: Graduate Texts in Mathematics
Inhalt: xx
426 S.
ISBN-13: 9780387947327
ISBN-10: 0387947329
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Sharpe, R. W.
Auflage: 1997
Hersteller: Springer US
Springer New York
Graduate Texts in Mathematics
Maße: 241 x 160 x 30 mm
Von/Mit: R. W. Sharpe
Erscheinungsdatum: 12.06.1997
Gewicht: 0,84 kg
preigu-id: 105102550
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