Natural parallel translation and connection associated to navigation data
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.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Fixed Point Theorems Analysis
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 4 January 2026
- Document type
- Preprint