Differential Geometry:Cartan's Generalization of Klein's Erlangen Program,(Graduate Texts in Mathematics) 微分几何:嘉当克莱因的埃朗根项目的推广

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北京朝阳

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作者R.W. Sharpe

出版社Springer

ISBN9780387947327

出版时间1997

装帧平装

上书时间2024-06-19

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商品描述: 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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