Natural parallel translation and connection associated to navigation data
Differential Geometry
2026-01-06 v1
Abstract
In this paper, we consider the geometric setting of navigation data and introduce a natural parallel translation using the Riemannian parallelism. The geometry obtained in this way has some nice and natural features: the natural parallel translation is homogeneous (but in general nonlinear), preserves the Randers type Finslerian norm constituted by the navigation data, and the holonomy group is finite-dimensional.
Cite
@article{arxiv.2601.01486,
title = {Natural parallel translation and connection associated to navigation data},
author = {Asma Mezrag and Zoltan Muzsnay and Csaba Vincze},
journal= {arXiv preprint arXiv:2601.01486},
year = {2026}
}