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Einführung in Die Geometrie Und Topologie by Werner Ballmann

Einführung in Die Geometrie Und Topologie

by Werner Ballmann
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Book cover type: Paperback
  • ISBN13: 9783034809856
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Birkhauser
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 163
  • Original Price: EUR 18.68
  • Language: German
  • Edition: 2. Aufl. 2018
  • Item Weight: 291 grams
  • BISAC Subject(s): Topology

Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Nach einer Einführung in grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie wird der Jordansche Kurvensatz für Polygonzüge bewiesen und damit eine erste Idee davon vermittelt, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschlie ende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension.

In der zweiten Auflage habe ich eine Reihe von Textstellen leicht überarbeitet und einige Fehler berichtigt.


Werner Ballmann ist Professor für Differntialgeometrie an der Universität Bonn und Direktor am Max-Planck-Institut für Mathematik in Bonn.

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