Metric structures in differential geometry

This text is an elementary introduction to differential geometry. The only prerequisites are a solid background in Calculus, linear algebra, and basic point-set topology. The first chapter covers the fundamentals of differentiable manifolds that are the bread and butter of differential geometry. All the usual topics are covered, culminating in Stokes? theorem together with some applications. The following chapters are devoted to fiber bundles, homotopy theory of fibrations, vector bundles, Euclidean bundles and Riemannian connections, and thena brief excursion into the realm of Riemannian geometry. The final chapter concludes with Chern-Weil theory, introducing the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. This book can be usedfor a one-semestercourse on manifolds or bundles, ora two- semester course in differential geometry. TOC:*Preface * Differntiable manifolds *Fiber bundles *Homotopy groups and bundles over spheres*Connections and curvature *Metric structures *Characteristic classes * Bibliography * Index