Overview

Das vorliegende Lehrbuch bietet eine moderne Einführung in die Differenzialgeometrie - etwa im Umfang einer einsemestrigen Vorlesung. Zunächst behandelt es die Geometrie von Flächen im Raum. Viele Beispiele schulen Leser in geometrischer Anschauung, deren wichtigste Klasse die Minimalflächen bilden. Zu ihrem Studium entwickeln die Autoren analytische Methoden und lösen in diesem Zusammenhang das Plateausche Problem. Es besteht darin, eine Minimalfläche mit vorgegebener Berandung zu finden. Als Beispiel einer globalen Aussage der Differenzialgeometrie beweisen sie den Bernsteinschen Satz. Weitere Kapitel behandeln die innere Geometrie von Flächen einschließlich des Satzes von Gauss-Bonnet, und stellen die hyperbolische Geometrie ausführlich dar. Die Autoren verknüpfen geometrische Konstruktionen und analytische Methoden und folgen damit einem zentralen Trend der modernen mathematischen Forschung. Verschiedene geistesgeschichtliche Bemerkungen runden den Text ab. Die Neuauflage wurde überarbeitet und aktualisiert. Hinweise und Errata auf Webseite des Autors: https://myweb.rz.uni-augsburg.de/~eschenbu/

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9783642385216

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Reviews

From the book reviews: The introduction presents an extensive history of geometry and a summary of the contents of the book. There are 12 main chapters as well as two additional chapters of needed material, a bibliography of 50 items, and an index of names, and subjects. The book is useful not only to students for independent work, but is also handy to the teaching staff for lecture preparation and conduct of seminars. (Kaarin Riives, zbMATH, Vol. 1286, 2014)

From the book reviews: </p> The introduction presents an extensive history of geometry and a summary of the contents of the book. There are 12 main chapters as well as two additional chapters of needed material, a bibliography of 50 items, and an index of names, and subjects. The book is useful not only to students for independent work, but is also handy to the teaching staff for lecture preparation and conduct of seminars. (Kaarin Riives, zbMATH, Vol. 1286, 2014)

"From the book reviews: ""The introduction presents an extensive history of geometry and a summary of the contents of the book. There are 12 main chapters as well as two additional chapters of needed material, a bibliography of 50 items, and an index of names, and subjects. ... The book is useful not only to students for independent work, but is also handy to the teaching staff for lecture preparation and conduct of seminars."" (Kaarin Riives, zbMATH, Vol. 1286, 2014)"

From the book reviews: The introduction presents an extensive history of geometry and a summary of the contents of the book. There are 12 main chapters as well as two additional chapters of needed material, a bibliography of 50 items, and an index of names, and subjects. The book is useful not only to students for independent work, but is also handy to the teaching staff for lecture preparation and conduct of seminars. (Kaarin Riives, zbMATH, Vol. 1286, 2014) From the book reviews: The introduction presents an extensive history of geometry and a summary of the contents of the book. There are 12 main chapters as well as two additional chapters of needed material, a bibliography of 50 items, and an index of names, and subjects. The book is useful not only to students for independent work, but is also handy to the teaching staff for lecture preparation and conduct of seminars. (Kaarin Riives, zbMATH, Vol. 1286, 2014)

Author Information

Prof. Dr. Jürgen Jost, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig Prof. Dr. Jost-Hinrich Eschenburg, Universität Augsburg

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