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Ueber Riemann's Theorie Der Algebraischen Functionen

Ueber Riemann's Theorie Der Algebraischen Functionen


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Auszug: ...entsprechen. Man ziehe zum Verstandnisse noch einmal die Figur (1) heran. Es folgt aus derselben, dass man die Umgebung eines formula-fachen Krenzungspunctes derart in formula Sectoren zerlegen kann, dass formula innerhalb jedes Sectors denselben Werthvorrath durchlauft. Daher werden oberhalb der betreffenden Stelle der formula Ebene formula Blatter der conformen Abbildung derart zusammenhangen, dass eine Umlaufung der Stelle von einem Blatte in ein zweites, von diesem in ein drittes fuhrt etc., und dass eine formula-malige Umlaufung derselben nothig wird, um zum Anfangspuncte zuruckzugelangen. Diess ist aber genau, was man gewohnlich als einen formula-fachen Verzweigungspunct bezeichnet(24). Dabei ist die Abbildung in diesem Puncte selbst naturlich keine conforme mehr; man beweist leicht, dass der Winkel, den irgend zwei auf der ursprunglichen Flache verlaufende sich im Kreuzungspuncte schneidende Curven mit einander bilden, auf der uber der formula-Ebene ausgebreiteten Riemann'schen Flache genau mit formula multiplicirt erscheint.- Aber zugleich erkennen wir die Bedeutung, welche diese mehrblattrige Flache fur unsere Zwecke beanspruchen kann. Alle Flachen, welche durch conforme Abbildung eindeutig aus einander hervorgehen, sind fur uns gleichbedeutend ( . 8). Wir konnen also die m-blattrige Flache uber der Ebene ebensogut zu Grunde legen, wie die bisher benutzte Flache, die wir uns ohne jedes singulare Vorkommniss frei im Raume gelegen vorstellten. Dabei kommt die Schwierigkeit, die man in dem Auftreten der Verzweigungspuncte erblicken konnte, von vorneherein in Wegfall: denn wir werden nur solche Stromungen auf der mehrblattrigen Flache in Betracht ziehen, welche sich in der Umgebung der Verzweigungspuncte derart verhalten, dass sie ruckwarts auf die im Raume gelegene ursprungliche Flache ubertragen dort keine anderen singularen Vorkommnisse darbieten, als die ohnehin gestatteten. Hierzu ist nicht einmal...


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Product Details
  • ISBN-13: 9781236701565
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 30
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1236701569
  • Publisher Date: 13 Sep 2013
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Weight: 73 gr


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