Differential Geometry: Cartan’s Generalization of Klein’s Erlangen Program (Graduate Texts in Mathematics, Vol. 166) (Graduate Texts in Mathematics, 166) by R.W. Sharpe | (PDF) Free Download

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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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a truly unique introduction to differential geometry. The role of Lie groups in differential geometry, which is often somewhat ambiguous in other introductory texts, is emphasized. Following the philosophy that geometry is determined by the symmetries we are interested in, Cartan geometry is a framework that encompasses nearly all differential geometric structures of interest, including Riemannian and semi-Riemannian geometry (the geometry of Relativity), CR geometry, conformal geometry, projective geometry, and many others. This is the best introductory text to Cartan geometry. A good second text on Cartan geometry once you are finished with this one is Cap and Slovak’s Parabolic Geometry.

⭐The book “Differential Geometry: Cartan’s Generalization of Klein’s Erlangen Program”, purchase from NRVBOOKSPLUS via AMAZON.COM, exceed my expectations! It’s completely new. It seems that no one has ever opened it. Also, I received the product very quickly. I’m so pleased with this purchase ande really recommend this seller.

⭐This is definitely a graduate school text. Though I believe the text can be read by a eager undergraduate. The text is about Differential Geometry.The subject matter demands that the reader read more than 1 book on the subject. This is a good introduction to a difficult but useful mathematical discipline.

⭐I was fortunate enough to have Sharpe as my supervisor at University of Toronto just when his book was published. His highly abstract thinking is very impressive and I have enjoyed immensely his first chapter on differential topology, which is my specialized area. Though his book branches off into realms that don’t particularly suit me, the beginnings of his book had given me great inspiration in my discipline in differential topology

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⭐la Géométrie Différentielle et Rieamannienne m’ont toujours fasciné;Differential Geometry, Riemannian Geometry, Differential and Riemannian Manifolds sont mes évangiles;ils sont tous excellents;que je puisse y puiser toute la richesse du savoir qui s’y trouve!

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Differential Geometry: Cartan’s Generalization of Klein’s Erlangen Program (Graduate Texts in Mathematics, Vol. 166) (Graduate Texts in Mathematics, 166) PDF Free Download
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Differential Geometry: Cartan’s Generalization of Klein’s Erlangen Program (Graduate Texts in Mathematics, Vol. 166) (Graduate Texts in Mathematics, 166) 1997 PDF Free Download
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