2025/03/30 by Prim Plansangkate, Plansangkate, Prim, Lenka Zalabová +1 · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2503.23442
openalex publication_date 2025/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.