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About this book
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.
Bibliographic Information
Book Title: Differential Geometry
Book Subtitle: Cartan's Generalization of Klein's Erlangen Program
Authors: R.W. Sharpe
Series Title: Graduate Texts in Mathematics
Publisher: Springer New York, NY
Copyright Information: Springer-Verlag New York 1997
Hardcover ISBN: 978-0-387-94732-7Published: 12 June 1997
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XX, 426