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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Introduction to Riemannian Manifolds
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Introduction to Riemannian Manifolds
John M. Lee (Broschiert, Englisch)
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Beschreibung
This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second edition has been adapted, expanded, and aptly retitled from Lee’s earlier book, Riemannian Manifolds: An Introduction to Curvature . Numerous exercises and problem sets provide the student with opportunities to practice… and develop skills; appendices contain a brief review of essential background material. While demonstrating the uses of most of the main technical tools needed for a careful study of Riemannian manifolds, this text focuses on ensuring that the student develops an intimate acquaintance with the geometric meaning of curvature. The reasonably broad coverage begins with a treatment of indispensable tools for working with Riemannian metrics such as connections and geodesics. Several topics have been added, including an expanded treatment of pseudo-Riemannianmetrics, a more detailed treatment of homogeneous spaces and invariant metrics, a completely revamped treatment of comparison theory based on Riccati equations, and a handful of new local-to-global theorems, to name just a few highlights. Reviews of the first edition: Arguments and proofs are written down precisely and clearly. The expertise of the author is reflected in many valuable comments and remarks on the recent developments of the subjects. Serious readers would have the challenges of solving the exercises and problems. The book is probably one of the most easily accessible introductions to Riemannian geometry. (M.C. Leung, MathReview ) The book’s aim is to develop tools and intuition for studying the central unifying theme in Riemannian geometry, which is the notion of curvature and its relation with topology. The main ideas of the subject, motivated as in the original papers, are introduced here in an intuitive and accessible way…The book is an excellent introduction designed for a one-semester graduate course, containing exercises and problems which encourage students to practice working with the new notions and develop skills for later use. By citing suitable references for detailed study, the reader is stimulated to inquire into further research. (C.-L. Bejan, zBMATH ) Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
05.08.2021
Sprache
Englisch
EAN
9783030801069
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Graduate Texts in Mathematics
Sonderedition
Nein
Autor
John M. Lee
Seitenanzahl
437
Auflage
2
Einbandart
Broschiert
Schlagwörter
Riemannian geometry, curvature, manifold, differential geometry textbook, graduate mathematics textbook, Riemannian geometry course textbook, Riemannian metrics, geodesics, Levi-Cevita connection, Riemannian submanifolds, Gauss-Bonnet theorem, Jacobi fields, comparison theory, curvature and topology, tensor
Thema-Inhalt
PBMP - Differentielle und Riemannsche Geometrie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer International Publishing, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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