Systeme halbkonzentrischer Kreise der euklidischen Ebene im komplexen Gebiet

All circles having the same tangent in one of the two absolute pointsJ, \(\bar J\) are said to be semi-concentric. They form a special net of conics Σ. By means of a complex conformal transformationT, Σ corresponds to the system Σ′ of the straight lines. Congruent circles in Σ correspond to parallel lines in Σ′. Moebius geometry in Σ is shown to be a model of the plane euclidean geometry. Furthermore, the plane is projected stereographically onto a Riemannian sphere; thenT corresponds to a biaxial involutionT ₁ which transforms the sphere into itself. The circles of Σ correspond to the intersections of the sphere with the planes passing throughJ. Finally, for a curvec having an ordinary point inJ, it follows thatc possesses inJ generally a well-defined radius of curvature but an infinite number of circles of curvature; one of them hyperosculatesc inJ. ByT, these circles correspond to a pencil of parallel lines. There are also considered examples of several special curves passing throughJ and \(\bar J\) .     

Bemerkungen zum Satz von Abramescu in der euklidischen und der isotropen Ebene

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Ein neuer Aufbau der euklidischen Geometrie in der affinen Ebene

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Einzigkeit der reellen und der komplexen projektiven Ebene

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Zur Theorie der algebraischen Gruppen der Geraden und der Ebene

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Orthogonale Kurvensysteme in der Ebene und auf der Kugel

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Exakte Paare und Kettenkomplexe

It is shown that the category of chain-complexes (of abelian groups) can be embedded as a full reflexive subcategory in the categoryEC of semi-regular exact couples. This situation gives rise to a monad on the categoryEC which has similar properties as the infinite symmetric product [4]. We use this monad and the process of Kan-extensions to study connections between the homology- and homotopyfunctors defined onEC. Furthermore we investigate homotopy-notions inEC and demonstrate that those constructed by W.S. Massey [9] and D.W. Kahn [6] are equivalent.     

Maximumprinzipähnliche Sätze der euklidischen und der affinen Flächentheorie

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Ueber cyklisch-projectivische Punktgruppen in der Ebene und im Raume

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