Einführung in Die Differentialgeometrie
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I. Vektoren, Determinanten, Matrizen.- 11. Vektorsunittie.- 12. Inneres Produkt.- 13. Polarprodukte, Determinanten.- 14. Äußeres Produkt.- 15. Matrizen.- II. Streifen und Linien.- 21. Begleitendes Breibein.- 22. Integralinvarianten eines Streifens.- 23. Drehung eines Streifens um seine Linie.- 24. Vierscheitelsatz.- 25. Schmiegkreis, Schmiegkugel.- 26. Formänderung eines Streifens.- 27. Aufgaben, Lehrsätze.- 28. Böschungslinien auf Drehquadriken.- 29. Die isoperimetrische Haupteigenschaft des Kreises.- III. Pfaffsche Formen.- 31. Altemierendes Produkt.- 32. Äußeres Differential.- 33. Zu einem Paar Pf äffscher Formen gehörige Ableitungen.- 34. Altemierende Differentialformen.- IV. Innere Flächenlehre.- 40. Geschichtliche Angaben.- 41. Grundgleichungen.- 42. Flächenmaß und Gesamtkrümmung.- 43. Biegungsinvarianz des Krümmungsmaßes.- 44. Die Integralformel von Gauß und Bonnet.- 45. Übertragung auf einer Fläche.- 46. Ausdehnung der Formel von Gauß und Bonnet auf eckige Bereiche.- 47. Die Formel von Gauß und Bonnet für geschlossene Flächen.- 48. Schiefwinklige lyiniennetze.- 49. Aufgaben, Lehrsätze.- V. Geodätische Linien.- 51. Geodätische als Kürzeste.- 52. Flächen festen Krümmungsmaßes.- 53. H. Poincarés Halbebene und die hyperbolische Geometrie.- 54. Parallellinien auf einer Fläche.- 55. Formeln von Green.- 56. Netze von Liouville.- 57. Verlauf der Geodätischen auf einer gewissen Fläche fester negativer Krümmung.- 58. Winkeltreue Abbildung.- 59. Aufgaben, Lehrsätze.- VI. Äußere Flächenlehre.- 61. Hauptkrümmungen.- 62. Krümmung der Flächenlinien.- 63. Der Satz von Du pin über rechtwinklige Flächennetze.- 64.Die winkeltreuen Abbildungen des Raumes.- 65. Schmieglinien.- 66. Schmieglinien auf geradlinigen Flächen.- 67. Starrheit der Eiflächen.- 68. Formänderungen einer Fläche.- 69. Aufgaben, Lehrsätze.- VII. Minimalflächen.- 71. Minimalflächen als Schiebflächen.- 72. Ermittlung der Schmieglinien und Krümmungslinien.- 73. Adjungierte Minimalflächen.- 74. Biegung von Minimalflächen.- 75. Formeln von Riemann und Weierstraß.- 76. Die Minimalflächen von Scherk.- 77. Die Minimalflächen von Enneper.- 78. Ausblick auf Plateaus Aufgabe.- 79. Aufgaben, Lehrsätze.- VIII. n-dimensionale Differentialgeometrie.- 81. Direkte Zerlegung der Differentiale.- 82. Lineare Übertragung.- 83. Flächenkurven.- 84. Erweiterung des Cartanschen Kalküls.- 85. Ableitungsgleichungen und Integrabilitätsbedingungen.- 86. Die Schmiegräume.- 87. Metrische Invarianten.- Anmerkungen.- Schrifttum.- Namen- und Sachverzeichnis.
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