TL;DR
This paper classifies all equidistant decompositions of the 2D Euclidean plane and sphere, providing a comprehensive understanding of submetry onto one-dimensional spaces.
Contribution
It offers a complete classification of equidistant decompositions in two-dimensional Euclidean and spherical geometries, advancing geometric decomposition theory.
Findings
Full classification of equidistant decompositions achieved
Identifies all possible submetries onto one-dimensional spaces
Enhances understanding of geometric decompositions in 2D Euclidean and spherical contexts
Abstract
We provide the full classification of equidistant decomposition of a two-dimensional Euclidean plane and a two-dimensional sphere.
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