# On some information geometric structures concerning Mercator projections

## TL;DR

This paper explores the information geometric structures underlying Mercator projections, highlighting the role of affine connections with torsion in describing loxodromes and reinterpreting Gaussian distributions within this framework.

## Contribution

It introduces the significance of affine connections with torsion in the geometric analysis of Mercator projections and revisits Gaussian distributions from this perspective.

## Key findings

- Affine connection with torsion describes auto-parallel paths on the globe surface.
- Loxodromes correspond to straight lines in Mercator maps.
- Relations between deformed functions and geometric structures are identified.

## 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.