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Glatte Mannigfaltigkeiten

In: Glatte Mannigfaltigkeiten

Author

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  • Claudio Gorodski

    (University of São Paulo, Institute of Mathematics and Statistics)

Abstract

Zusammenfassung Die Idee hinter dem Konzept der glatten Mannigfaltigkeit (der Dimension n) besteht zunächst darin, Punkte eines Sets lokal durch Angabe von n reellen Zahlen zu beschreiben – die sogenannten lokalen Koordinaten. Die Tatsache, dass wir mehr als ein System lokaler Koordinaten verwenden können, ermöglicht es uns, Sets mit komplizierterer Topologie zu betrachten. In einem zweiten Schritt möchten wir analytische Objekte auf diesen Sets konstruieren, die unabhängig von lokalen Koordinaten sind. Eine Motivation aus der Physik besteht darin, die Gleichungen der mathematischen Physik unabhängig von den gewählten Koordinaten zu schreiben. In diesem Kapitel stellen wir die grundlegenden Konstruktionen der Theorie der glatten Mannigfaltigkeiten vor und beweisen den Satz von Frobenius.

Suggested Citation

  • Claudio Gorodski, 2024. "Glatte Mannigfaltigkeiten," Springer Books, in: Glatte Mannigfaltigkeiten, chapter 0, pages 1-49, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-57161-9_1
    DOI: 10.1007/978-3-031-57161-9_1
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