Differential Geometry: Cartan's Generalization of Klein's Erlangen Program

Hardcover | November 21, 2000

byR.W. Sharpe, S. S. ChernPreface byS.S. Chern

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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.

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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. Alth...

Format:HardcoverDimensions:471 pages, 9.21 × 6.14 × 0.04 inPublished:November 21, 2000Publisher:Springer New York

The following ISBNs are associated with this title:

ISBN - 10:0387947329

ISBN - 13:9780387947327

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Table of Contents

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.