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Im vorliegenden Artikel werden die Integral- und Differentialinvarianten der Möbiusschen Gruppe (-Gruppe) hergeleitet. Weiter wird die Berührung einer in der Möbiusebene (-Ebene) gegebenen Kurve mit Kurven mit konstanter -Krümmung untersucht und es werden die -Analoge der Mittelpunkte der Krümmung, der Evolute und des Schmiegobjektes gefunden. Diese Problematik wird auch vom kinematischen Standpunkt interpretiert.
Im Artikel werden die Integral- und Differentialgrundinvarianten (Bogen, Krümmung) der ebenen Kurve angesichts der äquiformen Gruppe (-Gruppe) bei der Anwendung der komplexen Symbolik hergeleitet. Weiter werden die -minimalen Kurven, -Geraden und -Kreise von der -Geometrie festgestellt; im euklidischen Modell handelt es sich um die Geraden, Kreise und logarithmischen Spiralen.
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