Relativistic mechanics of constant curvature

TL;DR

This paper investigates the inverse variational problem for lines of constant curvature in pseudo-Euclidean spaces, with implications for relativistic particle mechanics.

Contribution

It introduces a novel approach to the inverse variational problem for constant curvature lines in pseudo-Euclidean spaces, connecting geometric and physical theories.

Findings

Results are physically meaningful for relativistic mechanics.

Extended the understanding of constant curvature lines in pseudo-Euclidean spaces.

Provided new insights into the geometric foundations of relativistic particle dynamics.

Abstract

We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of particles.