Differential geometry and homogeneous spaces / Kai Köhler

• Autore: Köhler, Kai
• Pubblicazione: Berlin, : Springer, 2024
• Descrizione fisica: 1 testo elettronico (X, 292 p. : ill.)
• Soggetto topico: 53-XX - Differential geometry [MSC 2020]; 53C05 - Connections, general theory [MSC 2020]; 53C20 - Global Riemannian geometry, including pinching [MSC 2020]; 53C30 - Differential geometry of homogeneous manifolds [MSC 2020]; 53C35 - Differential geometry of symmetric spaces [MSC 2020]; 83C05 - Einstein's equations (general structure, canonical formalism, Cauchy problems) [MSC 2020]
• Soggetto non controllato: Connection; Curvatures; De Rham Cohomology; Differential geometry; Differential topology; Fiber bundles; Geodesic; Global analysis; Homogeneous spaces; Lie algebra; Lie groups; Lorentz groups; Manifolds; Parallel transport; Relativity; Ricci curvature; Riemannian geometry; Symmetric spaces; Vector bundles
• Sommario/riassunto: This textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity. Starting with the basics of manifolds, it presents key objects of differential geometry, such as Lie groups, vector bundles, and de Rham cohomology, with full mathematical details. Next, the fundamental concepts of Riemannian geometry are introduced, paving the way for the study of homogeneous and symmetric spaces. As an early application, a version of the Poincaré–Hopf and Chern–Gauss–Bonnet Theorems is derived. The final chapter provides an axiomatic deduction of the fundamental equations of the General Theory of Relativity as another important application. Throughout, the theory is illustrated with color figures to promote intuitive understanding, and over 200 exercises are provided (many with solutions) to help master the material. (Dal sito dell'editore)
• Titolo autorizzato: Differential Geometry and Homogeneous Spaces
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: VAN00309985
• Lo trovi qui: Univ. Vanvitelli
• Localizzazioni e accesso elettronico: https://doi.org/10.1007/978-3-662-69721-4
• Serie: Universitext Berlin [etc] . -Springer , 1930-