Über ein Iterationsverfahren für zyklische Matrizen

Miroslav Šisler

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Laguerresche Differentialgeometrie und Kinematik

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In this paper the plane Laguerre’s geometry in the augmented plane of dual numbers is presented. Basic integral and differential invariants of $ℒ$ -curves in the plane are deduced, i.e. the $ℒ$ -curve arc, $ℒ$ -curvature, $ℒ$ -minimal curves, $ℒ$ -circle. Furthermore the contact of $ℒ$ -curves, $ℒ$ -osculating circle, $ℒ$ -evolute of a curve and some special $ℒ$ -motions are studied from the point of view of $ℒ$ -Differential geometry.

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Double points on characteristics

Otto Röschel (1995)

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Double Points on Characteristics. A fixed surface $Φ$ of a moving space $Σ$ will envelope a surface of the fixed space $Σ^{'}$ , if we move $Σ$ with respect to $Σ^{'}$ . In the general case at each moment of the one-parameter motion there exists a curve $c$ on $Φ$ , along which the position of $Φ$ and the enveloped surface are in contact. In the paper we study the interesting special case, where $c$ has some double point $P \in Φ$ . This depends on relations between differential geometric properties in the neighbourhood...