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Metric Structures in Differential Geometry

Metric Structures in Differential Geometry


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About the Book

This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.

Review :
From the reviews: "The book gives an introduction to the basic theory of differentiable manifolds and fiber bundles The book is well written. The presentation is clear, detailed and essentially self-contained. This book is suitable for senior undergraduate and graduate students. It can be used for a course on manifolds and bundles, or a course in differential geometry." (M. Burkhardt, Zeitschrift f r Analysis und ihre Anwendungen, 1, 2005) "This text is an introduction to the theory of differentiable manifolds and fiber bundles provides a comprehensive overview of differentiable manifolds concepts are illustrated in detail for bundles over spheres This book can be used for a one-semester course on manifolds or bundles, or a two-semester course in differential geometry." (L'enseignement math matique, 50:1-2, 2004) "This book is based on the author s graduate-level lecture notes. One of the strengths of this book is the fact that the author manages in a 220-page volume to cover important themes in Riemannian geometry and fiber bundles. The book contains some nice examples . The topics are well-closed and the content is well-organized. This clearly written book is an excellent source for teaching a course in differential geometry . It is a worthwhile addition to any mathematical library." (Stere Ianus, Zentralblatt MATH, Vol. 1083, 2006) "This text should be an elementary introduction to differential geometry. The style is rather concise and many facts are shifted to 165 nontrivial exercises. The book is very well written and can be recommended to those who want to learn the topic quickly and actively." (EMS Newsletter, June, 2005) "This book is a carefully written text for an introductory graduate course on differentiable manifolds, fiber bundles and Riemannian geometry. This book is a thorough and insightful introduction to modern differential geometry with many interesting examples and exercises that illustrate key concepts effectively; it is highly recommended by t


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Product Details
  • ISBN-13: 9781468495898
  • Publisher: Springer My Copy UK
  • Publisher Imprint: Springer My Copy UK
  • Height: 234 mm
  • Weight: 340 gr
  • ISBN-10: 1468495895
  • Publisher Date: 18 Mar 2004
  • Binding: Paperback
  • Spine Width: 13 mm
  • Width: 156 mm


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