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Introduction to Riemannian Manifolds

BuchKartoniert, Paperback
437 Seiten
Englisch
Springererschienen am05.08.20212. Aufl.
âThis textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds.mehr
Verfügbare Formate
BuchGebunden
EUR69,54
BuchKartoniert, Paperback
EUR53,49

Produkt

KlappentextâThis textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds.
Details
ISBN/GTIN978-3-030-80106-9
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2021
Erscheinungsdatum05.08.2021
Auflage2. Aufl.
ReiheGraduate Texts in Mathematics
Seiten437 Seiten
SpracheEnglisch
IllustrationenXIII, 437 p. 210 illus.
Artikel-Nr.49807682

Inhalt/Kritik

Inhaltsverzeichnis
Preface.- 1. What Is Curvature?.- 2. Riemannian Metrics.- 3. Model Riemannian Manifolds.- 4. Connections.- 5. The Levi-Cevita Connection.- 6. Geodesics and Distance.- 7. Curvature.- 8. Riemannian Submanifolds.- 9. The Gauss-Bonnet Theorem.- 10. Jacobi Fields.- 11. Comparison Theory.- 12. Curvature and Topology.- Appendix A: Review of Smooth Manifolds.- Appendix B:  Review of Tensors.- Appendix C: Review of Lie Groups.- References.- Notation Index.- Subject Index.mehr
Kritik
"One interesting aspect of the book is the decision of which audience to target it towards. ... Overall, this would make a very appropriate text for a graduate course, or a programme of individual study in Riemannian geometry, whether to give a thorough treatment of the fundamentals, or to introduce the more advanced topics in global geometry." (Robert J. Low, Mathematical Reviews, November, 2019)
"This material is carefully developed and several useful examples and exercises are included in each chapter. The reviewer's belief is that this excellent edition will become soon a standard text for several graduate courses as well as an frequent citation in articles." (Mircea Crâsmareanu, zbMATH 1409.53001, 2019)mehr

Autor

John "Jack" M. Lee is a professor of mathematics at the University of Washington. Professor Lee is the author of three highly acclaimed Springer graduate textbooks : Introduction to Smooth Manifolds, (GTM 218) Introduction to Topological Manifolds (GTM 202), and Riemannian Manifolds (GTM 176). Lee's research interests include differential geometry, the Yamabe problem, existence of Einstein metrics, the constraint equations in general relativity, geometry and analysis on CR manifolds.