Eichfeldtheorie: Eine Einfuhrung in Die Differentialgeometrie Auf Faserbundeln (Springer-lehrbuch Masterclass) - Softcover

From the reviews:

“The aim of the book is to introduce students with ... background in Riemannian geometry to the theory of connections on principal bundles and holonomy. ... The exposition of the material is clear and very detailed. Many examples and figures illustrate the concepts and theorems. At the end of each chapter there are exercises. Most of them provide further interesting examples. Solutions are given at the end of the book. This book is definitely a welcome addition to the German textbook market.” (Thomas Püttmann, Zentralblatt MATH, Vol. 1175, 2010)

“This textbook provides a thorough introduction into the theory of connections on principal fiber bundles and holonomy. ... Each chapter of this carefully prepared text is closed by a number of well-selected exercises. Their solutions are given at the end of the book together with an appendix collecting the necessary prerequisites from Riemannian geometry.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 165 (3-4), March, 2012)

Dieses Lehrbuch führt in die Differentialgeometrie auf Faserbündeln ein. Es vermittelt die mathematischen Grundlagen zur Eichfeldtheorie in der theoretischen und mathematischen Physik. Neben Lie-Gruppen und homogenen Räumen behandelt das Buch lokal-triviale Faserungen, grundlegende Begriffe der Differentialrechnung auf Faserbündeln sowie Holonomiegruppen. Es ist ideal als Begleiter für einsemestrige Differentialgeometrie-Vorlesungen im Mathematik- oder Physik-Hauptstudium. Viele Beispiele, Aufgaben und Lösungen helfen, den Stoff zu vertiefen.