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Nervensystem: Erkrankungen Des Zentralen Nervensystems I

Nervensystem: Erkrankungen Des Zentralen Nervensystems I

          
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About the Book

Die innere Geometrie einer Flache ist die Lehre von denjenigen Eigenschaften, die bei isometrischen Abbildungen ungeandert bleiben, also nur von ihrer ersten Fundamentalform abhangen. Sie wurde von C. F. GAUSS durch die Entdeckung begrundet, dass das Produkt der Hauptkrummungsradien einer Flache eine isometrische Invariante ist. B. RIEMANN dehnte diese Theorie in seiner Habilitationsschrift auf mehr dimensionale und damit gleichzeitig auf abstrakte Mannigfaltigkeiten aus. Wahrend man zunachst nur das Studium solcher Mannigfaltigkeiten in Betracht zog, deren Bogenelement durch die Quadratwurzel aus einer quadratischen Differentialform gegeben ist, entwickelte P. FINSLER in seiner Dissertation die innere Geometrie auf der Grundlage eines all gemeinen Bogenelementes, eine Moglichkeit, die bereits B. RIEMANN erkannt hatte. Seit den klassischen Untersuchungen von J. HADAMARD uber Flachen konstanter negativer Krummung und von D. HILBERT uber die Existenz von Extremalen bei Variationsproblemen setzte sich die Erkenntnis immer mehr durch, dass ein grosser Teil der Methoden, insbesondere diejenigen, welche in der Differentialgeometrie im Grossen entwickelt worden sind, nur die topologische und metrische Struktur der Mannigfaltigkeiten, nicht aber ihre Differenzierbarkeitsstruktur be notigen. Der von FREcHET geschaffene Begriff des metrischen Raumes ermoglichte es, die innere Geometrie auf einer von Differenzierbarkeits voraussetzungen freien Grundlage zu stellen. Zunachst stand jedoch die Topologie der metrischen Raume im Vordergrund des Interesses. Erst mit K. MENGER setzte ein systematisches Studium der isometrischen Invarianten ein. Inzwischen ist eine umfangreiche Literatur entstanden. Die Hauptergebnisse sind in den drei Buchern von A. D. ALEXANDROW[6J, L. M. BLuMENTHAL [1J und H."


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Product Details
  • ISBN-13: 9783540026723
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Height: 0 mm
  • No of Pages: 520
  • Series Title: Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover)
  • Weight: 700 gr
  • ISBN-10: 354002672X
  • Publisher Date: 01 Jan 1961
  • Binding: Hardback
  • Language: German
  • Returnable: N
  • Spine Width: mm
  • Width: 0 mm


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