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Laguerre’s differential geometry and kinematics. (Laguerresche Differentialgeometrie und Kinematik.) (German) Zbl 0840.53013
The author studies differential geometric properties of curves in the sense of plane Laguerre geometry over dual numbers. He gives formulas to determine the “\(L\)-curve arc” and the “\(L\)-curvature”. Then he considers \(L\)-minimal curves and \(L\)-osculating circles. All is done in analogy to the case of Laguerre geometry over complex numbers.
MSC:
53A35 Non-Euclidean differential geometry
51B15 Laguerre geometries
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