Differential geometry : bundles, connections, metrics and curvature / Clifford Henry Taubes

The book by the well-known mathematician is an excellent introduction to differential geometry for first year graduate students or advanced undergraduate students. The topics covered in the book are: smooth manifolds, Lie groups, vector bundles, metrics on vector bundles, Riemannian metrics, geodesics on Riemannian manifolds, principal bundles, covariant derivatives and connections, holonomy, curvature polynomials and characteristic classes, Riemannian curvature tensor, complex manifolds, holomorphic submanifolds of a complex manifold and Kähler metrics. The presentation is as much as possible self-contained. The author gives detailed proofs of basic results. The book has 298 pages and consists of 19 chapters. Each chapter contains a detailed bibliography for additional reading. (Zentralblatt)

Références bibliogr. en fin de chapitres. Index