On some information geometric structures concerning Mercator projections
arXiv:1905.11214 · doi:10.1016/j.physa.2019.121591
Abstract
Some information geometric structures concerning the Mercator projections are studied. It is known that a loxodrome on the surface of the globe is related to the straight line on a Mercator map by the Mercator projection. It is not well known that an affine connection with torsion plays a fundamental role to describe an auto-parallel path on the surface. Based on these information geometric structures, Gauss distribution is reconsidered from the view point of the affine connection with a torsion. Some relations with deformed functions are also pointed out.
17pages, 3 figures, resubmitted to Physica A