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Glatte Mannigfaltigkeiten by Claudio Gorodski

Glatte Mannigfaltigkeiten

by Claudio Gorodski
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Book cover type: Paperback
  • ISBN13: 9783031571602
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer Spektrum
  • Publisher Imprint: Springer Spektrum
  • Publication Date:
  • Pages: 162
  • Original Price: EUR 42.05
  • Language: German
  • Edition: 1. Aufl. 2024
  • Item Weight: 350 grams
  • BISAC Subject(s): Mathematical Analysis

Dieses prägnante und praxisorientierte Lehrbuch präsentiert die Grundlagen der Mathematik auf glatten Mannigfaltigkeiten. Glatte Mannigfaltigkeiten sind ein Schlüsselkonzept in der Mathematik und weit verbreitet: Sie treten auf als Riemannsche Mannigfaltigkeiten in der Differentialgeometrie; als Raum-Zeiten in der Allgemeinen Relativitätstheorie; als Phasenräume und Energieniveaus in der Mechanik; als Definitionsbereiche von gewöhnlichen Differentialgleichungen in dynamischen Systemen; als Lie-Gruppen in Algebra und Geometrie; und in vielen anderen Bereichen.Das Buch präsentiert zunächst die grundlegenden Begriffe und Sätze zu glatten Mannigfaltigkeiten und kulminiert mit dem Frobenius-Theorem, bevor es Tensoren auf Mannigfaltigkeiten behandelt (einschlie lich einer Darstellung der äu eren Ableitung von Differentialformen).Es behandelt dann Lie-Gruppen und Lie-Algebren und geht kurz auf homogene Mannigfaltigkeiten ein.Integration auf Mannigfaltigkeiten, Erläuterungen des Stokes-Theorems und der de-Rham-Kohomologie sowie Grundlagen der Differentialtopologie vervollständigen dieses Werk. Es enthält auch Übungen im gesamten Text, um den Lesern zu helfen, die Theorie zu verstehen, sowie anspruchsvollere Probleme für diejenigen, die Herausforderungen mögen, am Ende jedes Kapitels. Konzipiert für einen einsemestrigen Kurs über differentielle Mannigfaltigkeiten und Lie-Gruppen, der von vielen Graduiertenprogrammen weltweit angeboten wird, ist es eine wertvolle Ressource für Studierende und Dozenten gleicherma en.

Die Übersetzung wurde mit Hilfe von künstlicher Intelligenz durchgeführt. Eine anschlie ende menschliche Überarbeitung erfolgte vor allem in Bezug auf den Inhalt.


Claudio Gorodski ist Professor am Institut für Mathematik und Statistik der Universität São Paulo, Brasilien. Er hat einen Doktortitel in Mathematik (1992) von der University of California in Berkeley, USA, und eine Habilitation (1998) von der Universität São Paulo, Brasilien. Seine Forschungsinteressen umfassen Lie-Transformationsgruppen in der Riemannschen Geometrie, Geometrie von Untermannigfaltigkeiten, Riemannsche symmetrische Räume und sub-Riemannsche Geometrie.

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