John M. Lee

Riemannian Manifolds

An Introduction to Curvature

• Broschiertes Buch

Produktbeschreibung

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Produktdetails

• Graduate Texts in Mathematics 176
• Verlag: Springer, Berlin
• 1997.
• Seitenzahl: 226
• Erscheinungstermin: August 2006
• Englisch
• Abmessung: 235mm x 157mm x 14mm
• Gewicht: 368g
• ISBN-13: 9780387983226
• ISBN-10: 0387983228
• Artikelnr.: 07277332

Inhaltsangabe

What Is Curvature?.- Review of Tensors, Manifolds, and Vector Bundles.- Definitions and Examples of Riemannian Metrics.- Connections.- Riemannian Geodesics.- Geodesics and Distance.- Curvature.- Riemannian Submanifolds.- The Gauss-Bonnet Theorem.- Jacobi Fields.- Curvature and Topology.

Rezensionen

This book is very well writen, pleasant to read, with many good illustrations. It deals with the core of the subject, nothing more and nothing less. Simply a recommendation for anyone who wants to teach or learn about the Riemannian geometry. Nieuw Archief voor Wiskunde, September.