Metric Structures in Differential Geometry (Softcover Reprint of the Original 1st 2004)Paperback - Softcover Reprint of the Original 1st 2004, 29 November 2010

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.