Conserved quantities of distinguished curves on conformal sphere
Differential Geometry
2025-04-29 v2 Mathematical Physics
math.MP
Abstract
We give conserved quantities of two generalizations of conformal circles on the conformal sphere. One generalization concerns curves carrying a distinguished parallel tractor along them, which can be used to construct the conserved quantities. The other is the class of curves satisfying the conformal Mercator equation, the conserved quantities of which are computed using Lagrangian formalism. The two generalizations are not disjoint, and our main result is the relation between their conserved quantities. Explicit examples are also presented.
Keywords
Cite
@article{arxiv.2503.23442,
title = {Conserved quantities of distinguished curves on conformal sphere},
author = {Prim Plansangkate and Lenka Zalabová},
journal= {arXiv preprint arXiv:2503.23442},
year = {2025}
}
Comments
Minor changes - some typos are corrected