Laguerre’s differential geometry and kinematics. (Laguerresche Differentialgeometrie und Kinematik.) (German) Zbl 0840.53013

Jankovský, Zdeněk

Math. Bohem. 120, No. 1, 29-40 (1995).

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.

Reviewer: Otto Röschel (Graz)

MSC:

53A35	Non-Euclidean differential geometry
51B15	Laguerre geometries

Keywords:

Laguerre geometry in the isotropic plane; differential geometric properties of curves