For the Laguerre geometry in the dual plane, invariant arc length is shown to arise
naturally through the use of a pair of distance functions. These distances are useful for identifying
equivalence classes of curves, within which the extremal curves are proved to be strict maximizers
of Laguerre arc length among three-times differentiable curves of constant signature in a prescribed
isotopy class. For smoother curves, it is shown that Laguerre curvature determines the distortion of
the distance functions. These results extend existing work for the Möbius geometry in the complex
plane.
@article{1294789786,
author = {Barrett, David E. and Bolt, Michael},
title = {Laguerre Arc Length from Distance Functions},
journal = {Asian J. Math.},
volume = {14},
number = {1},
year = {2010},
pages = { 213-234},
language = {en},
url = {http://dml.mathdoc.fr/item/1294789786}
}
Barrett, David E.; Bolt, Michael. Laguerre Arc Length from Distance Functions. Asian J. Math., Tome 14 (2010) no. 1, pp. 213-234. http://gdmltest.u-ga.fr/item/1294789786/