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Differentialgeometrie

In: Anschauliche Geometrie

Author

Listed:
  • David Hilbert
  • Stephan Cohn-Vossen

Abstract

Zusammenfassung Bisher haben wir geometrische Gebilde in ihrer Gesamtstruktur betrachtet. Die Differentialgeometrie stellt ein prinzipiell anderes Verfahren der Forschung dar. Wir wollen nämlich jetzt Kurven und Flächen zunächst nur in der unmittelbaren Umgebung irgendeines ihrer Punkte beschreiben. Zu diesem Zweck vergleichen wir diese Umgebung mit einem möglichst einfachen Gebilde, etwa einer Geraden, einer Ebene, einem Kreis oder einer Kugel, die sich der Kurve in der betrachteten Umgebung möglichst eng anschmiegt; so entsteht z. B. der bekannte Begriff der Tangente einer Kurve in einem Punkt.

Suggested Citation

  • David Hilbert & Stephan Cohn-Vossen, 1996. "Differentialgeometrie," Springer Books, in: Anschauliche Geometrie, edition 0, chapter 0, pages 151-239, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-19948-6_4
    DOI: 10.1007/978-3-642-19948-6_4
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