Metric Structures in Differential Geometry (Graduate Texts in Mathematics)
Publisher: Springer | ISBN 10: 1441919139 | 2010 | PDF | 226 pages | 6.8 MB
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.