Differential geometry : Cartan's generalization of Klein's Erlangen program / R.W. Sharpe ; foreword by S.S. Chern.

Format:

Book

Author/Creator:

Sharpe, R. W. (Richard W.)

Series:

Graduate texts in mathematics ; 166.

Graduate texts in mathematics ; 166

Language:

English

Subjects (All):

Geometry, Differential.

Physical Description:

xix, 421 pages : illustrations ; 25 cm.

Place of Publication:

New York : Springer, [1997]

Summary:

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 generalises" (= 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.

Notes:

Includes bibliographical references (pages [411]-415) and index.

ISBN:

0387947329

OCLC:

34356972