Foundations of Differential Geometry, Volume 1

This two-volume introduction to differential geometry, part of Wiley’s popular <i>Classics Library</i>, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. <b>Volume 1</b> presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The <b>second volume</b> continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.