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Differentialgeometrie von Kurven und Flchen
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Dieses Lehrbuch, verfat von Manfredo P. do Carmo, Professor fr Mathematik am Instituto de Matematica Pura e Aplicada (IMPA) in Rio de Janeiro, ist eine Einfhrung in die elementare Differentialgeometrie, die mehr Wert auf die grundlegenden geometrischen Tatsachen als auf den Formalismus legt. In jedem Kapitel werden einige einfache fundamentale Ideen in den Mittelpunkt gestellt. So sttzt sich Kapitel 2 auf den Begriff einer regulren Flche in R3, ein Modell fr den allgemeinen Begriff einer differenzierbaren Mannigfaltigkeit. Die Betrachtung der Gau- Abbildung in Kapitel 3 fhrt zu einem Einblick in die lokale Geometrie von Flchen in R3. Kapitel 4 zeigt, wie sich die innere Geometrie der Flchen aus dem Begriff der kovarianten Ableitung entwickeln lt; hier wird auf den allgemeinen Begriff eines Zusammenhangs in der Riemannschen Geometrie vorbereitet.
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