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Analytische Und Konstruktive Differentialgeometrie by Erwin Kruppa

Analytische Und Konstruktive Differentialgeometrie

by Erwin Kruppa
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Book cover type: Paperback
  • ISBN13: 9783709178683
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 191
  • Original Price: EUR 56.07
  • Language: German
  • Edition: Softcover Repri
  • Item Weight: 327 grams
  • BISAC Subject(s): General

Das vorliegende Lehrbuch "Analytische und konstmktive Differentialgeometrie" gliedert sich in zwei Teile. Der erste Teil "Analytische Differentialgeometrie" ist eine EinfUhrung in die analytische, allgemeine Theorie der Raumkurven und FHi.chen, der Strahlflachen, Strahlkongruenzen und Strahlkomplexe im euklidi- schen Raum. Er soll eine ausreichende Grundlage fUr ein tieferes Eindringen in die Differentialgeometrie liefern. Diese Zweckbestimmung laBt naturgemaB dem Verfasser nur wenig freien Spielraum. Doch wurden manche Einzelheiten neu gestaltet. Insbesondere wurde die Theorie der Strahlflachen in einer von mir in einigen Arbeiten entwickelten Methode dargestellt, die die Theorie der Raum- kurven als Sonderfall der Theorie der Strahlflachen erscheinen laBt. 1m zweiten Teil "Konstruktive Differentialgeometrie" wird in der Differential- geometrie die seit den Uranfangen der Geometrie getibte Methode angewendet, die das im Geiste moglichst klaF gedachte, wenn moglich graphisch versinnlichte geometrische Objekt mittels Synthese und Rechnung erforscht. In ihrer Frtih- zeit war die Differentialgeometrie stark anschaulich-konstruktiv ausgerichtet. Diese Richtung muBte aber in den Hintergrund treten, je mehr die moderne Ent- wicklung in abstrakte Gebiete fUhrte, die sich nur wenig oder gar nicht anschau- li.ch erfassen lassen. Sie kam auch unverdient in MiBkredit, als miBbrauchlich in ihrem Namen viel Unfug mit "unendlich klein en GroBen" getrieben wurde. Es liegt in der Natur der Sache, daB in der Differentialgeometrie die anschaulich- konstruktive Methode nur auf einer analytischen Grundlage angewendet werden kann, da ihre Begriffsbi1dungen auf Voraussetzungen tiber Differenzierbarkeit beruhen. Die auf diesem Wege zu gewinnenden Ergebnisse sind daher bloB Er- ganzungen zur analytischen Theorie.

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