Differential geometry / Richard W. Sharpe (1997)

Public ISBD Titre : Differential geometry : cartan's generalization of klein's erlangen program Type de document : texte imprimé Auteurs : Richard W. Sharpe, Auteur Editeur : Berlin ; London ; Cham : Springer Année de publication : 1997 Collection : Graduate texts in mathematics num. 166 Importance : XIX-421 p. Présentation : ill. Format : 25 cm ISBN/ISSN/EAN : 978-0-387-94732-7 Note générale : With 104 ill. Bibliogr. Index Langues : Anglais (eng) Mots-clés : Geometry, Differential Géométrie différentielle Index. décimale : 514.7 Géométrie différentielle. Méthodes algébriques et analytiques en géométrie Résumé : This text presents a systematic and well-motivated development of differential geometry leading to the global version of Cartan connections. The material is presented at a level accessible to a first-year graduate student. The first four chapters provide a complete development of the fundamentals of differential topology, foliations, Lie groups, and homogeneous spaces. Chapter 5 studies Cartan geometries which generalize homogeneous spaces in the same way that Riemannian geometry generalizes Euclidean geometry. One of the beautiful facets of Cartan geometries is that curvature appears as an exact local measurement of "broken symmetry." The last three chapters study Riemannian geometry, conformal geometry, and projective geometry. Topics included in the five appendices are a comparison of Cartan and Ehresmann connections, and the derivation of the divergence and curl operators from symmetry considerations Note de contenu : - 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 - Mobius Geometry - Projective Geometry Differential geometry : cartan's generalization of klein's erlangen program [texte imprimé] / Richard W. Sharpe, Auteur . - Berlin ; London ; Cham : Springer, 1997 . - XIX-421 p. : ill. ; 25 cm. - (Graduate texts in mathematics; 166) . ISBN : 978-0-387-94732-7 With 104 ill. Bibliogr. Index Langues : Anglais (eng) Mots-clés : Geometry, Differential Géométrie différentielle Index. décimale : 514.7 Géométrie différentielle. Méthodes algébriques et analytiques en géométrie Résumé : This text presents a systematic and well-motivated development of differential geometry leading to the global version of Cartan connections. The material is presented at a level accessible to a first-year graduate student. The first four chapters provide a complete development of the fundamentals of differential topology, foliations, Lie groups, and homogeneous spaces. Chapter 5 studies Cartan geometries which generalize homogeneous spaces in the same way that Riemannian geometry generalizes Euclidean geometry. One of the beautiful facets of Cartan geometries is that curvature appears as an exact local measurement of "broken symmetry." The last three chapters study Riemannian geometry, conformal geometry, and projective geometry. Topics included in the five appendices are a comparison of Cartan and Ehresmann connections, and the derivation of the divergence and curl operators from symmetry considerations Note de contenu : - 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 - Mobius Geometry - Projective Geometry

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Code-barres	Cote	Support	Localisation	Section	Disponibilité	Etat_Exemplaire
046778	514.7 SHA	Papier	Bibliothèque Centrale	Mathématiques	Disponible