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On some information geometric structures concerning Mercator projections

Author

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  • Wada, Tatsuaki

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.

Suggested Citation

  • Wada, Tatsuaki, 2019. "On some information geometric structures concerning Mercator projections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    • Handle: RePEc:eee:phsmap:v:531:y:2019:i:c:s0378437119309379
    DOI: 10.1016/j.physa.2019.121591
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    Cited by:

    1. Wada, Tatsuaki & Scarfone, Antonio M. & Matsuzoe, Hiroshi, 2021. "An eikonal equation approach to thermodynamics and the gradient flows in information geometry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    2. Jun Jian & Zheng Sun & Kai Sun, 2024. "An Intelligent Automatic Sea Forecasting System Targeting Specific Areas on Sailing Routes," Sustainability, MDPI, vol. 16(3), pages 1-20, January.

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